   Chapter 2.4, Problem 130E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Proof Prove that if lim Δ x → 0 f ( c + Δ x ) = f ( c ) then f is continuous at c.

To determine

To prove: f is continuous at x=c, if limΔx0f(c+Δx)=f(c).

Explanation

Given: limΔx0f(c+Δx)=f(c)

Formula used:

Condition for continuity,

limxcf(x)=limxc+f(x)=f(c)

Proof:

Consider the provided limit,

limΔx0f(c+Δx)=f(c)

f(c) is defined.

To calculate limxcf(x), let x=c+Δx.

If xc, then Δx0

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