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Let f(x) = x – sin x. (a) Show that f increases on (-o, 00). Use the result in part (a) to show that sin x < x on (0, 0) and (b) sin x > x on (-0,0).

Let f(x) = x – sin x. (a) Show that f increases on (-o, 00). Use the result in part (a) to show that sin x < x on (0, 0) and (b) sin x > x on (-0,0).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3. Let \( f(x) = x - \sin x \). (a) Show that \( f \) increases on \( (-\infty, \infty) \). (b) Use the result in part (a) to show that \( \sin x < x \) on \( (0, \infty) \) and \( \sin x > x \) on \( (-\infty, 0) \).
Transcribed Image Text:3. Let \( f(x) = x - \sin x \). (a) Show that \( f \) increases on \( (-\infty, \infty) \). (b) Use the result in part (a) to show that \( \sin x < x \) on \( (0, \infty) \) and \( \sin x > x \) on \( (-\infty, 0) \).
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