Explanation Formula used: (1). Continuity checklist: In order for f to be continuous at a , the following three conditions must hold. i. f ( a ) is defined ( a is in the domain of f ). ii. lim x → a f ( x ) exists. iii. lim x → a f ( x ) = f ( a ) (the value of f equals the limit of f at a ). (2). Theorem 2.10: Polynomial and Rational functions. i. A polynomial function is continuous for all x . ii. A rational function (a function of the form p q , where p and q are polynomials) is continuous for all x for which q ( x ) ≠ 0 . Calculation: The continuity of the function h ( x ) = x 2 − 9 at a = 3 is calculated as follows. Substitute x = 3 in h ( x ) = x 2 − 9 , h ( 3 ) = 3 2 − 9 = 9 − 9 = 0 The function h ( 3 ) is defined

Calculus: Early Transcendentals, 2nd Edition

2nd Edition

ISBN: 9780321965165

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 2, Problem 49RE

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Whether the function h(x)=x2−9 is continuous at a=3 by using the continuity checklist to justify the answer.

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Chapter 2, Problem 48RE

Chapter 2, Problem 50RE

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Chapter 2 Solutions

Calculus: Early Transcendentals, 2nd Edition

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Whether the function h ( x ) = x 2 − 9 is continuous at a = 3 by using the continuity checklist to justify the answer.

Solution Summary: The author explains the continuity checklist to determine whether the function h(x)=sqrt

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Whether the function h(x)=x2−9 is continuous at a=3 by using the continuity checklist to justify the answer.

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Chapter 2 Solutions