Suppose ƒ : E → R, p is a limit point of E, and lim f(x) exists. Prove that there exist x-p M> 0 and 8 >0 such that |f(x)| ≤ M when x € E with 0 < |x − p| < 8.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.1: Limits
Problem 59E
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(3) Suppose f: E → R, p is a limit point of E, and lim f(x) exists. Prove that there exist
x-p
M> 0 and 8 >0 such that f(x)| ≤ M when x € E with 0 < x − p| <d.
Transcribed Image Text:(3) Suppose f: E → R, p is a limit point of E, and lim f(x) exists. Prove that there exist x-p M> 0 and 8 >0 such that f(x)| ≤ M when x € E with 0 < x − p| <d.
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