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

    $-\infty$ −2 $\displaystyle -{{2}\over{3}}$ Does not exist. $\infty$

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

    −2 4 9 1

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

    $-\infty$ Does not exist. −1 $\infty$

  4. Find $\displaystyle \lim_{x\rightarrow -2}{{{f\left(x\right)+6}\over{x-1}}}$.

    Does not exist. $-\infty$ $\infty$ −1

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

    −12 −3 4 Does not exist.


Department of Mathematics
Last modified: 2026-08-31