Exercise 13. Assume that f,g: [a, b] → R are differentiable on [a, b], pe (a, b). Assume thatf'(x)lim f(x) = lim g(x) = 0,and= L.limx→p g'(x)x-px-pProve thatf(x)limx→p g(x)= L.

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Answered: Exercise 13. Assume that f,g: [a, b] →…

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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Exercise 13. Assume that f,g: [a, b] → R are differentiable on [a, b], pe (a, b). Assume that lim f(x) = lim g(x) = 0, f'(x) and = L. x-p x-p lim x→p g'(x) Prove that f(x) lim x→p g(x) = L.