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

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

  2. Find $\displaystyle \lim_{x\rightarrow -2}{{{f\left(x\right)+7}\over{x+1}}}$.

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

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

    5 Does not exist. −45 −9

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

    9 16 −3 4

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

    $\displaystyle \sqrt{2}$ $\displaystyle \sqrt{5}$ 2 Does not exist.


Department of Mathematics
Last modified: 2026-05-04