Q. 58 - Calculus

Question

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits. 

$\underset{x\to \infty }{\lim }\frac{x-4}{x^2-4}$

Step-by-Step Solution

Answer

The value is $\underset{x\to \infty }{\lim }\frac{x-4}{x^2-4}=\frac{1}{4}$ and graph is,

Step 1. Given information.

The given function is $\underset{x\to \infty }{\lim }\frac{x-4}{x^2-4}$

Step 2. Graph of the function.

The graph of the function is,

$$\begin{gathered} As x\to \infty , f\left(x\right)=\frac{1}{4} \\ Therefore, \\ \underset{x\to \infty }{\lim }\frac{x-4}{x^2-4}=\frac{1}{4} \end{gathered}$$