Suppose the function \( f \) has the property that there exists a number \( B \) such that\[|f(x) - f(c)| \leq B |x - c|\]for all \( x \) in the interval \( (c - p, c + p) \). Prove that \( f \) is continuous at \( c \).

Suppose the function f has the property that there exists a number B such that |f(x)-f(c)|≤B|x – c|…

Answered: Suppose the function f has the property…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Suppose the function f has the property that there exists a number B such that |S(x) – f(c)| < B|x – c| for all x in the interval (c – p, c + p). Prove that f is con- tinuous at c.