## Related questions with answers

Question

In given problem, find the indicated limit or state that it does not exist. In many cases, you will want to do some algebra before trying to evaluate the limit.

$\lim _{x \rightarrow 2} \frac{x^2-4}{x^2+4}$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Using Statements $(1)$, $(4)$ and $(8)$ from the Main Limit Theorem, we have

$\lim_{x\rightarrow 2}(x^{2}+4)=8$

so we can apply Statement $(7)$ to evaluate the given limit:

$\lim_{x\rightarrow 2}\frac{x^{2}-4}{x^{2}+1}=\frac{\lim_{x\rightarrow 2}(x^{2}-4)}{\lim_{x\rightarrow 2}(x^{2}+4)}=\frac{0}{8}=0.$

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