Explanation Given information : G ( x ) = { a x + b i f x < 0 3 i f x = 0 2 sin ( a cos − 1 x ) i f 0 < x < 1 , 0 < a < 1 Concept Involved: For a piecewise function to be continuous for all x values given, the end points of the interval need to have same height. The height of the left side function should be equal to the height of right side function at boundary point. Here in this problem for the function to be continuous at x = 0 both of the below equations should be equal. a x + b = 3 → 1 s t e q u a t i o n 3 = 2 sin ( a cos − 1 x ) → 2 n d e q u a t i o n Calculation: Description Steps Substituting x = 0 in first equation a ( 0 ) + b = 3 Solving for b 0 + b = 3 b = 3 Substituting x = 0 in second equation 3 = 2 sin ( a cos − 1 0 ) Substituting the value π 2 for

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 2.3, Problem 41PS

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Tofind:the value of constants a and b .

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Chapter 2.3, Problem 40PS

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Chapter 2 Solutions

Calculus

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Tofind : the value of constants a and b .

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Chapter 2 Solutions