Question

In Problems 7– 42, find each limit algebraically.

$\underset{x\to 0}{\lim }\frac{x^2-4}{x^2+4}$.

Short answer

The answer is -1.

Step-by-step solution

Step. 1 Given Information

Given is the limit on which x tends to 0 and the function given is:

$\frac{x^2-4}{x^2+4}$

Step. 2 Solving the limit

Firstly, we check whether the given function is in indeterminant form or not.

Since if we put $x=0$then it doesn't create any indeterminant form. So, to solve the limit we can directly put the value of x in the function. So,

$$\begin{gathered} \underset{x\to 0}{\lim }\frac{x^2-4}{x^2+4}=\frac{0-4}{0+4} \\ =\frac{-4}{4}=-1. \end{gathered}$$