Chapter 11.4, Problem 1E

To determine

To calculate:

The limit of $f$ .

Answer to Problem 1E

The required limit of $f$ as $x$ approaches to infinity is $\underset{x\to \infty }{\lim }f\left(x\right)=5$ .

Explanation of Solution

Given Information:

Horizontal Line $y=5$

Calculation:

Suppose $f\left(x\right)$ be a function and $L_1$ and $L_2$ be real numbers, then the statements $\underset{x\to \infty }{\lim }f\left(x\right)=L_1$ and $\underset{x\to \infty }{\lim }f\left(x\right)=L_2$ denotes the limit at infinity.

To find the limit of $f$ as $x$ approaches to infinity.

Since, $y=5$ is a horizontal asymptote to the right of the graph if function $f$ . Then,

  $y=\underset{x\to \infty }{\lim }f\left(x\right)$ but $y=5$ , then

  $\underset{x\to \infty }{\lim }f\left(x\right)=5$

Therefore, the required limit of $f$ as $x$ approaches to infinity is $\underset{x\to \infty }{\lim }f\left(x\right)=5$ .