Suppose that $\displaystyle \lim_{x\rightarrow -2}{f\left(x\right)}=-3$ and $\displaystyle \lim_{x\rightarrow -2}{g\left(x\right)}=3$ . Then answer the following questions.

  1. Find $\displaystyle \lim_{x\rightarrow -2}{{{f\left(x\right)+1}\over{x+1}}}$.

    $\infty$ 2 Does not exist. $-\infty$

  2. Find $\displaystyle \lim_{x\rightarrow -2}{\left(f\left(x\right)+4\,x^2+2\,x\right)\, \left(g\left(x\right)+3\right)}$.

    6 Does not exist. 54 9

  3. Find $\displaystyle \lim_{x\rightarrow -2}{\left(g\left(x\right)+f\left(x\right)+2 \right)^2}$.

    9 4 2 1

  4. Find $\displaystyle \lim_{x\rightarrow -2}{\sqrt{g\left(x\right)+1}}$.

    4 Does not exist. 2 $\displaystyle \sqrt{7}$

  5. Find $\displaystyle \lim_{x\rightarrow -2}{{{f\left(x\right)+7}\over{x+2}}}$.

    Does not exist. 4 $-\infty$ $\infty$


Department of Mathematics
Last modified: 2025-07-29