Chapter 11.4, Problem 62E

To determine

To identify: True or false.

Answer to Problem 62E

Given statement “Rational function $f$ has a horizontal asymptote to the right, then the limit of $f\left(x\right)$ as $x$ approaches to $-\infty$ exists” is false.

Explanation of Solution

Given information:

Given statement:

Rational function $f$ has a horizontal asymptote to the right, then the limit of $f\left(x\right)$ as $x$ approaches to $-\infty$ exists.

A limit is basically value of function $f\left(x\right)$ when the function $f\left(x\right)$ becomes arbitrary close to a unique number $L$ as $x$ approaches $c$ from the either side.

For determining the statement whether true or false.

Since if the rational function has a horizontal asymptote to the right.

Then the limit of the function $f\left(x\right)$ as $x$ approaches to $-\infty$ exists.

Which means $\underset{x\to \infty }{\lim }f\left(x\right)=L$ exists.

Thus, given statement is false.