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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-

Calculus For The Life Sciences
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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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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