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

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

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

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

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

    −3 16 4 9

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

    7 −49 Does not exist. −7


Department of Mathematics
Last modified: 2026-06-20