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 9RQ
To determine

To find: Whether the statement “A function can have two different horizontal asymptotes” is true or false.

Expert Solution

Answer to Problem 9RQ

The statement “A function can have two different horizontal asymptotes” is true.

Explanation of Solution

Given information:

The given statement is “A function can have two different horizontal asymptotes”.

Calculation:

The horizontal asymptote is a horizontal tangent line to the curve at infinity. The line y=L is called a horizontal asymptote of the curve y=f(x) if either limxf(x)=L or limxf(x)=L .

Consider the function

  f(x)=tan1(x)

Calculate the value of limxf(x)

  limxf(x)=limxtan1(x)=π2

Hence, y=π2 is a horizontal asymptote to the curve.

Calculate the another value of limxf(x)

  limxf(x)=limxtan1(x)=π2

Hence, y=π2 is another horizontal asymptote to the curve.

These results are observed from the below graph.

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2, Problem 9RQ

Therefore, the statement “A function can have two different horizontal asymptotes” is true.

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