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-
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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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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