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Math
CalculusSingle Variable Calculus: Early Transcendentals8th Edition

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Chapter 2, Problem 15RQ
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Solutions

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Problem 3RCC
Problem 4RCC
Problem 5RCC
Problem 6RCC
Problem 7RCC
Problem 8RCC
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Problem 10RCC
Problem 11RCC
Problem 12RCC
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Problem 14RCC
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Problem 13RE
Problem 14RE
Problem 15RE
Problem 16RE
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Problem 18RE
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Problem 1P
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Problem 7P
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Problem 9P
Problem 10P
Problem 11P
Problem 12P
Problem 13P
Problem 14P
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If the line x = 1 is a vertical asymptote of y = f(x), then f is not de tined at 1.

To determine

Whether the statement, “If the line x=1 is a vertical asymptote of y=f(x), then f is not defined at 1 ” is true or false.

Explanation

Definition used: A piecewise defined function is one which is defined not by a single equation, but by two or more. Each equation is valid for some interval.

Reason:

Given that the vertical asymptote x=1. The denominator of the function must be x−1.

The function may be f(x)=1x−1. Here f(1) is not defined.

But the given statement is false since the below example disproves the given statement.

Consider the piecewise defined function,

Let f(x)={1x−1     <

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Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.2 P-1E
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