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

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

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.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 48E

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Question

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Let f RR 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 limx→∞ f'(x) = 0, prove that limx→∞ g(x) = 0 by using the Mean Value Theo-
rem.

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