Consider the function f: (-∞, 0) U (0, ∞) → R defined by f(x) = x sin(). A. For every x in the domain of f, the following compound inequality holds:-|| ≤ f(x) ≤ |x|. Explain. B. Use the observation from Part A along with The Squeeze Theorem to deduce that limx→o f(x) = 0.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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r sin (1).
1. Consider the function ƒ: (-∞, 0) U (0, ∞) → R defined by f(x)
A. For every x in the domain of f, the following compound inequality holds: −|x| ≤ f(x) ≤ |x|. Explain.
B. Use the observation from Part A along with The Squeeze Theorem to deduce that limx→o f(x) = 0.
= X
Transcribed Image Text:r sin (1). 1. Consider the function ƒ: (-∞, 0) U (0, ∞) → R defined by f(x) A. For every x in the domain of f, the following compound inequality holds: −|x| ≤ f(x) ≤ |x|. Explain. B. Use the observation from Part A along with The Squeeze Theorem to deduce that limx→o f(x) = 0. = X
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