Problem #2: Prove the following theorem:Theorem 1. Suppose that f, g, h: A → R and c is an accumulation point of A. Ifandf(x) ≤ g(x) ≤ h(x) for all x Є Alim f(x) = lim h(x) = L,x→cx cthen the limit of g(x) as x →c exists andlim g(x) = L.x c

Answered: Image /qna-images/answer/8985270e-278f-4346-86f5-d286e7c421ea.jpg

Answered: Theorem 1. Suppose that f, g, h: A → R…

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.CR: Chapter 9 Review

Problem 6CR

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Theorem 1. Suppose that f, g, h: A → R and c is an accumulation point of A. If and f(x) ≤ g(x) ≤ h(x) for all x Є A lim f(x) = lim h(x) = L, x c x c then the limit of g(x) as x → c exists and lim g(x) = L. x→c