Prove the following case of L'Hospital's Rule: let ƒ,g be differentiable on (a, +) for some a ER. Suppose that 1. lim g(x) = +; 2. lim I→+∞ 9'(x) f'(x) = +0. Show that f(x) lim = +0. z→+00 g(x)
Prove the following case of L'Hospital's Rule: let ƒ,g be differentiable on (a, +) for some a ER. Suppose that 1. lim g(x) = +; 2. lim I→+∞ 9'(x) f'(x) = +0. Show that f(x) lim = +0. z→+00 g(x)
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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Transcribed Image Text:Prove the following case of L'Hospital's Rule: let f, g be differentiable on (a, +0) for some a ER. Suppose that
1. lim g(x) =+∞;
f'(x)
2. lim
z+00 9'(x)
= +0.
Show that
f(x)
lim
= +0.
x→+0 g(x)
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