BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2, Problem 11RQ
To determine

To find: 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.

Expert Solution

Answer to Problem 11RQ

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

Explanation of Solution

Given information:

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

Calculation:

The line x=a is called a vertical asymptote of the curve y=f(x) if at least one of the following statements is true.

  limxaf(x)= and limxaf(x)=

It is an asymptote means that the line never touches that point on a graph. So if it never touches 1 then it cannot be defined it could come to 1.0000000000000001 , but never one.

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

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