# Determining a Limit when given 2 limits

Let$\lim\limits_{x\to -3} f(x) =2$ and $\lim\limits_{x\to -3} g(x) =9$

Find $\lim\limits_{x\to -3} [\frac{[f(x)]^2}{2+g(x)}]$

I believe that the answer is $4/11$ but I wanted to check with you guys if I did it correctly. I plugged in the $2$ and the $9$ and essentially solved using basic math. Thanks for any helpful tips or advice!

• Yes, you are correct. Limits can be exchanged with multiplication, division, addition, etc (in other words, the limit of a product is the product of the limits, and so on). – florence Jun 3 '16 at 1:31

The answer is indeed $4/11$:
$\dfrac{2^2}{2+9} = \frac{4}{11}$