Explanation Given : f ( x ) = x 3 and δ ≤ 1 Concept used: Continuity: The function f from ℝ to ℝ is continuous at a point p ∈ ℝ if given ε > 0 thereexist δ > 0 such that if 0 < | p − x | < δ then | f ( p ) − f ( x ) | < ε . Calculation: f ( x ) = x 3 be a given function and δ ≤ 1 Now suppose c ≥ 0 ; the proof for c ≤ 0 is similar. Given ε > 0 let δ = min ( 1 , ε ( 3 c 2 + 3 c + 1 ) ) If 0 < | p − x | < δ , then since δ ≤ 1 it has p − 1 < x < p + 1 Then | p 3 x

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 1.4, Problem 90P

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To show:A fuction f is continuous on its domainby using a delta epsilon proof.

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Chapter 1.4, Problem 89P

Chapter 1.4, Problem 91P

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Chapter 1 Solutions

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A fuction f is continuous on its domainby using a delta epsilon proof.

Solution Summary: The author explains how a fuction f is continuous on its domain by using the delta epsilon proof.

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Chapter 1 Solutions