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 g ( x ) = { x 2 − 16 x − 4 if x ≠ 4 8 if x = 4 at a = 4 is calculated as follows. Substituting x = 4 in g ( x ) = { x 2 − 16 x − 4 if x ≠ 4 8 if x = 4 , g ( 4 ) = 8

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Chapter 2, Problem 50RE

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Whether the function g(x)={x2−16x−4 if x≠48 if x=4 is continuous at a=4 by using the continuity checklist to justify the answer.

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Chapter 2, Problem 49RE

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Chapter 2 Solutions

Calculus: Early Transcendentals (2nd Edition)

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Whether the function g ( x ) = { x 2 − 16 x − 4 if x ≠ 4 8 if x = 4 is continuous at a = 4 by using the continuity checklist to justify the answer.

Solution Summary: The author explains the continuity checklist to determine whether the function g(x)=lx is continuous at a=4.

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Whether the function g(x)={x2−16x−4 if x≠48 if x=4 is continuous at a=4 by using the continuity checklist to justify the answer.

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Chapter 2 Solutions