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Prove the "o0/0" case of l'Hopital's rule. That is, prove that if f : I → R and g : I → R are differentiable functions satisfying lim f(x) = lim g(x) for a E I, then 0 = f'(x) f(x) x→a g(x) lim = L implies lim = L. x>a g'(x)

Prove the "o0/0" case of l'Hopital's rule. That is, prove that if f : I → R and g : I → R are differentiable functions satisfying lim f(x) = lim g(x) for a E I, then 0 = f'(x) f(x) x→a g(x) lim = L implies lim = L. x>a g'(x)

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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I've attached L'hopitales rule. Thank you.

(L’Hopital's Rule). Suppose I is an open interval containing a, and f, g : I → R are differentiable on I, except possibly at a. Then, if lim f(x) = 0 and lim g(x) = 0, or if lim f(x) to and lim g(x) = ±o, then f(x) f'(x) lim lim g(x) x→a g'(x)' f'(x) provided the limit lim exists. g'(x)
Transcribed Image Text:(L’Hopital's Rule). Suppose I is an open interval containing a, and f, g : I → R are differentiable on I, except possibly at a. Then, if lim f(x) = 0 and lim g(x) = 0, or if lim f(x) to and lim g(x) = ±o, then f(x) f'(x) lim lim g(x) x→a g'(x)' f'(x) provided the limit lim exists. g'(x)
Prove the "o/0" case of l'Hopital's rule. That is, prove that if f : I → R and g : I → R are differentiable functions satisfying lim f(x) = = lim g(x) for a E I, then f' (x) gʻ(x) f(x) x→a g(x) lim = L implies lim L.
Transcribed Image Text:Prove the "o/0" case of l'Hopital's rule. That is, prove that if f : I → R and g : I → R are differentiable functions satisfying lim f(x) = = lim g(x) for a E I, then f' (x) gʻ(x) f(x) x→a g(x) lim = L implies lim L.
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