Chapter 13, Problem 17RE

To determine

To find: the value of the limit.

Answer to Problem 17RE

The value of $\underset{x\to \infty }{\lim }\frac{2x}{x-4}$ is $2$.

Explanation of Solution

Given information:

The limit is $\underset{x\to \infty }{\lim }\frac{2x}{x-4}$.

Calculation: to find the value of limit first divide and then simplify,

  $\begin{array}{l}\underset{x\to \infty }{\lim }\frac{2x}{x-4}=\underset{x\to \infty }{\lim }\frac{2}{1-\frac{4}{x}}\text{ [divide by }x]\\ \underset{x\to \infty }{\lim }\frac{2x}{x-4}=\frac{2}{1-0}\text{ [substitute]}\\ \underset{x\to \infty }{\lim }\frac{2x}{x-4}=2\text{ [simplify]}\end{array}$

Thus, the value is $2$.