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Concept
Continuity in mathematics refers to a function that does not have any abrupt changes in value, meaning it can be drawn without lifting the pencil from the paper. It is a fundamental concept in calculus and analysis, underpinning the behavior of functions and their limits, and is essential for understanding differentiability and integrability.
Concept
The Lipschitz condition is a mathematical criterion used to ensure the uniqueness and stability of solutions to differential equations by bounding the rate at which functions can change. It is a stronger form of continuity, requiring that the absolute difference between function values is proportional to the distance between inputs, with a constant known as the Lipschitz constant acting as the proportionality factor.
Concept
|f(x) - L| < εT|f(x) - L| < εh|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εs|f(x) - L| < εi|f(x) - L| < εl|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε-|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < ε-|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εs|f(x) - L| < εi|f(x) - L| < εl|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε-|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < εf|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εz|f(x) - L| < εa|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εh|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε>|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εa|f(x) - L| < εl|f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εl|f(x) - L| < εu|f(x) - L| < εs|f(x) - L| < ε,|f(x) - L| < ε |f(x) - L| < εp|f(x) - L| < εr|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εg|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < εr|f(x) - L| < εi|f(x) - L| < εg|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εs|f(x) - L| < ε-|f(x) - L| < εf|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εa|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < εr|f(x) - L| < εi|f(x) - L| < εg|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εf|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εa|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε |f(x) - L| < εf|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εh|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < ε-|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εu|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε>|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εu|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < ε.|f(x) - L| < ε |f(x) - L| < εI|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εt|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εh|f(x) - L| < εa|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < εf|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < εf|f(x) - L| < ε(|f(x) - L| < εx|f(x) - L| < ε)|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < εp|f(x) - L| < εp|f(x) - L| < εr|f(x) - L| < εo|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εh|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < ε>|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εL|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εx|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < εp|f(x) - L| < εp|f(x) - L| < εr|f(x) - L| < εo|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εh|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εc|f(x) - L| < ε>|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εf|f(x) - L| < ε,|f(x) - L| < ε |f(x) - L| < εf|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εe|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εy|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εs|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εn|f(x) - L| < εu|f(x) - L| < εm|f(x) - L| < εb|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εe|f(x) - L| < ε>|f(x) - L| < εP|f(x) - L| < εo|f(x) - L| < εs|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εu|f(x) - L| < εm|f(x) - L| < εb|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εε|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε,|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εh|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εi|f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εs|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εu|f(x) - L| < εm|f(x) - L| < εb|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εδ|f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εu|f(x) - L| < εc|f(x) - L| < εh|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εh|f(x) - L| < εa|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εw|f(x) - L| < εh|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < ε0|f(x) - L| < ε-|f(x) - L| < εx|f(x) - L| < ε-|f(x) - L| < εc|f(x) - L| < ε-|f(x) - L| < εd|f(x) - L| < ε>|f(x) - L| < ε0|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < ε |f(x) - L| < ε||f(x) - L| < εx|f(x) - L| < ε |f(x) - L| < ε-|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < ε||f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < ε |f(x) - L| < εδ|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε||f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < ε0|f(x) - L| < ε-|f(x) - L| < εx|f(x) - L| < ε-|f(x) - L| < εc|f(x) - L| < ε-|f(x) - L| < εd|f(x) - L| < ε>|f(x) - L| < ε0|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < ε |f(x) - L| < ε||f(x) - L| < εx|f(x) - L| < ε |f(x) - L| < ε-|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < ε||f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < ε |f(x) - L| < εδ|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε||f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εb|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εk|f(x) - L| < εm|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εo|f(x) - L| < εv|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε_|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < εa|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε |f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < ε4|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < εu|f(x) - L| < εr|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < ε-|f(x) - L| < εp|f(x) - L| < εo|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < εs|f(x) - L| < εs|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εs|f(x) - L| < ε_|f(x) - L| < εa|f(x) - L| < εc|f(x) - L| < εt|f(x) - L| < εi|f(x) - L| < εv|f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < ε_|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε_|f(x) - L| < ε_|f(x) - L| < εj|f(x) - L| < εs|f(x) - L| < ε8|f(x) - L| < εA|f(x) - L| < εc|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εs|f(x) - L| < εt|f(x) - L| < εy|f(x) - L| < εl|f(x) - L| < εe|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εt|f(x) - L| < εe|f(x) - L| < εx|f(x) - L| < εt|f(x) - L| < ε-|f(x) - L| < εu|f(x) - L| < εn|f(x) - L| < εd|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < ε-|f(x) - L| < εo|f(x) - L| < εf|f(x) - L| < εf|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε:|f(x) - L| < ε |f(x) - L| < ε4|f(x) - L| < εp|f(x) - L| < εx|f(x) - L| < ε;|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εd|f(x) - L| < ε |f(x) - L| < ε=|f(x) - L| < ε |f(x) - L| < ε"|f(x) - L| < εd|f(x) - L| < εy|f(x) - L| < εn|f(x) - L| < εa|f(x) - L| < εm|f(x) - L| < εi|f(x) - L| < εc|f(x) - L| < ε_|f(x) - L| < εl|f(x) - L| < εi|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < εe|f(x) - L| < εd|f(x) - L| < ε_|f(x) - L| < εp|f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εa|f(x) - L| < εs|f(x) - L| < εe|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εa|f(x) - L| < εr|f(x) - L| < εg|f(x) - L| < εe|f(x) - L| < εt|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < ε_|f(x) - L| < εb|f(x) - L| < εl|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < εk|f(x) - L| < ε"|f(x) - L| < ε |f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εl|f(x) - L| < ε=|f(x) - L| < ε"|f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εo|f(x) - L| < εp|f(x) - L| < εe|f(x) - L| < εn|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε |f(x) - L| < εn|f(x) - L| < εo|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εr|f(x) - L| < ε"|f(x) - L| < ε
|f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < ε |f(x) - L| < εh|f(x) - L| < εr|f(x) - L| < εe|f(x) - L| < εf|f(x) - L| < ε=|f(x) - L| < ε/|f(x) - L| < εc|f(x) - L| < εo|f(x) - L| < εn|f(x) - L| < εc|f(x) - L| < εe|f(x) - L| < εp|f(x) - L| < εt|f(x) - L| < ε/|f(x) - L| < ε0|f(x) - L| < ε-|f(x) - L| < εx|f(x) - L| < ε-|f(x) - L| < εc|f(x) - L| < ε-|f(x) - L| < εd|f(x) - L| < ε>|f(x) - L| < ε0|f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < ε |f(x) - L| < ε||f(x) - L| < εx|f(x) - L| < ε |f(x) - L| < ε-|f(x) - L| < ε |f(x) - L| < εc|f(x) - L| < ε||f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < ε |f(x) - L| < εδ|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εa|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε<|f(x) - L| < ε/|f(x) - L| < εs|f(x) - L| < εp|f(x) - L| < εa|f(x) - L| < εn|f(x) - L| < ε>|f(x) - L| < ε,|f(x) - L| < ε |f(x) - L| < εi|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < εf|f(x) - L| < εo|f(x) - L| < εl|f(x) - L| < εl|f(x) - L| < εo|f(x) - L| < εw|f(x) - L| < εs|f(x) - L| < ε |f(x) - L| < εt|f(x) - L| < εh|f(x) - L| < εa|f(x) - L| < εt|f(x) - L| < ε |f(x) - L| < ε||f(x) - L| < εf|f(x) - L| < ε(|f(x) - L| < εx|f(x) - L| < ε)|f(x) - L| < ε |f(x) - L| < ε-|f(x) - L| < ε |f(x) - L| < εL|f(x) - L| < ε||f(x) - L| < ε |f(x) - L| < ε<|f(x) - L| < ε |f(x) - L| < εε|f(x) - L| < ε.|f(x) - L| < ε
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The Heine-Cantor Theorem states that if a function is continuous on a compact metric space, then it is uniformly continuous. This result is significant because it provides a stronger form of continuity that is applicable in many areas of analysis and topology, ensuring that small changes in input lead to small changes in output uniformly across the entire space.
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A metric space is a set equipped with a metric, which is a function that defines a distance between any two elements in the set, satisfying properties like non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. metric spaces provide a framework for analyzing concepts of convergence, continuity, and compactness in a general setting, extending beyond the familiar Euclidean space.
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Compactness in mathematics, particularly in topology, refers to a property of a space where every open cover has a finite subcover, which intuitively means the Space is 'small' or 'bounded' in a certain sense. This concept is crucial in analysis and topology as it extends the notion of closed and bounded subsets in Euclidean spaces to more abstract spaces, facilitating various convergence and continuity results.
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Boundedness refers to the property of a set or function where there exists a limit beyond which the values do not extend. It is a fundamental concept in mathematics and analysis, providing constraints that simplify the study of complex systems by ensuring that they remain within certain limits.
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Function limits describe the behavior of a function as its input approaches a particular value, and they are fundamental in defining continuity, derivatives, and integrals in calculus. Understanding limits allows us to analyze and predict the behavior of functions at points where they may not be explicitly defined.
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Real analysis is a branch of mathematics that deals with the rigorous study of real numbers and real-valued functions, focusing on concepts such as limits, continuity, and convergence. It provides the foundational framework for calculus and is essential for understanding the behavior of functions and sequences in a real-number context.
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Topology is a branch of mathematics that studies the properties of space that are preserved under continuous transformations such as stretching and bending, but not tearing or gluing. It provides a foundational framework for understanding concepts of convergence, continuity, and compactness in various mathematical contexts.
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A continuous function is one where small changes in the input result in small changes in the output, ensuring no abrupt jumps or breaks in the graph of the function. This property is crucial for analysis in calculus and real analysis, as it ensures the function behaves predictably under limits and integrals.
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A continuous function is one where small changes in the input lead to small changes in the output, ensuring there are no sudden jumps or breaks in its graph. Continuity is a fundamental property in calculus and analysis, crucial for understanding limits, derivatives, and integrals.
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Continuity and discontinuity are fundamental concepts in mathematics and philosophy, describing whether a function or process is unbroken or has interruptions. Understanding these concepts helps in analyzing the behavior of functions in calculus and the nature of change in various scientific and philosophical contexts.
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A continuous path refers to a function from a closed interval into a topological space that is continuous, meaning there are no abrupt changes or breaks in the path. This concept is fundamental in topology and analysis, providing a framework for understanding connectedness and continuity in various mathematical contexts.
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A continuous map is a function between two topological spaces that preserves the notion of closeness, meaning the preimage of every open set is open. This concept is fundamental in topology as it allows for the comparison of different spaces by examining how they can be transformed into one another without 'tearing' or 'gluing' points together.
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Continuity on an interval ensures that a function behaves predictably without any abrupt changes in value, meaning it is unbroken and smooth over that interval. For a function to be continuous on a closed interval, it must be continuous at every point within the interval and have limits matching the function's value at the interval's endpoints.
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Lipschitz continuity is a condition on functions that ensures they do not oscillate too wildly by requiring the rate of change between any two points to be bounded by a constant, known as the Lipschitz constant. This property is crucial in various fields such as numerical analysis and optimization as it guarantees the existence and uniqueness of solutions to differential equations and stability in optimization algorithms.
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The Lipschitz constant is a measure of the maximum rate of change of a function, ensuring that the function does not oscillate too wildly, which is crucial for stability and convergence in numerical methods. It is particularly important in optimization and machine learning, where it helps in understanding the behavior of algorithms and functions, ensuring they are well-behaved and predictable.
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The modulus of continuity is a function that measures the uniform continuity of a function by quantifying how much the function's value can change with respect to changes in its input. It provides a precise way to describe the rate at which a function becomes continuous over its domain, offering insights into the function's smoothness and potential for approximation by simpler functions.
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The Law of Continuity, rooted in calculus and mathematical analysis, asserts that continuous functions maintain their values without abrupt changes, ensuring that small changes in input lead to small changes in output. This principle is fundamental in understanding the behavior of functions and is pivotal in fields like physics and engineering where smooth transitions are essential.
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The Hölder condition is a mathematical criterion used to measure the smoothness of functions, particularly in the context of real analysis and partial differential equations. It generalizes the concept of Lipschitz continuity by introducing a parameter that allows for a more flexible description of how a function's values can vary with changes in its input.
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Hölder continuity is a property of functions that quantifies how uniformly continuous they are, characterized by a Hölder condition involving a non-negative exponent that dictates the rate of continuity. This concept generalizes the notion of Lipschitz continuity by allowing for a broader range of exponents, thus providing a more flexible framework for analyzing function behavior, especially in fractal and complex systems.
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An epsilon neighborhood is a set of all points within a specified distance, epsilon, from a given point in a metric space. It is essential for understanding concepts like continuity, limits, and convergence in mathematical analysis and topology.
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