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Let ƒ : R → R be a function that is differentiable on (a, ∞), where a is any real onstant. Let g: RR be a function defined by g(x) = f(x+1) – f(x). limx→∞ f'(x) = 0, prove that limx→∞ g(x) = 0 by using the Mean Value Theo-

Let ƒ : R → R be a function that is differentiable on (a, ∞), where a is any real onstant. Let g: RR be a function defined by g(x) = f(x+1) – f(x). limx→∞ f'(x) = 0, prove that limx→∞ g(x) = 0 by using the Mean Value Theo-

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let ƒ : R → R be a function that is differentiable on (a, ∞), where a is any real constant. Let g : R → R be a function defined by g(x) = f(x+1) – f(x). If limä→∞ ƒ'(x) = 0, prove that limä→∞ g(x) = 0 by using the Mean Value Theo- rem.
Transcribed Image Text:Let ƒ : R → R be a function that is differentiable on (a, ∞), where a is any real constant. Let g : R → R be a function defined by g(x) = f(x+1) – f(x). If limä→∞ ƒ'(x) = 0, prove that limä→∞ g(x) = 0 by using the Mean Value Theo- rem.
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