(a) Explanation Given information: The figure is, Figure (1) Calculation: If x is the central angle of circle of radius r = 1 then, x = A B 1 = A B The ABC is a square triangle which has hypotenuse A B (b) To determine To show: The proof that | sin x | < | x | (c) To determine To show: The proof that sin x is continuous at x = 0 . (d) To determine To show: The proof that sin x is continuous for all real x .

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Limits

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Question

Chapter 2, Problem 90SP

(a)

To determine

To show: The proof that sinx<x

(b)

To determine

To show: The proof that |sinx|<|x|

(c)

To determine

To show:The proof that sinx is continuous at x=0 .

(d)

To determine

To show: The proof that sinx is continuous for all real x .

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Chapter 2, Problem 89SP

Chapter 2, Problem 91SP

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Chapter 2 Solutions

Calculus

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