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By following the steps below, prove that if lim-c f(x) = L and limrc g(x) = M = 0, -hen limx→eg() = - (a) Prove that there exists > 0 such that if 0 < x- c < 6, then g(x)| ≥ |M/2 > 0.

By following the steps below, prove that if lim-c f(x) = L and limrc g(x) = M = 0, -hen limx→eg() = - (a) Prove that there exists > 0 such that if 0 < x- c < 6, then g(x)| ≥ |M/2 > 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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2. By following the steps below, prove that if limr c f(x) = L and limrc g(x) = M = 0, then lime (= g(x) (a) Prove that there exists > 0 such that if 0 < x- c < 6, then g(x) > M/2 > 0. (b) Prove that f(x) L g(x) M LIANI = |f(x) M - Lg(x)| < |f(x)M − LM| + |LM — Lg(x)| g(x) M g(x) M f(x) 9x en 1- g(x)|
Transcribed Image Text:2. By following the steps below, prove that if limr c f(x) = L and limrc g(x) = M = 0, then lime (= g(x) (a) Prove that there exists > 0 such that if 0 < x- c < 6, then g(x) > M/2 > 0. (b) Prove that f(x) L g(x) M LIANI = |f(x) M - Lg(x)| < |f(x)M − LM| + |LM — Lg(x)| g(x) M g(x) M f(x) 9x en 1- g(x)|
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