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

    −3 4 9 16

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

    Does not exist. $-\infty$ $\infty$ −1 $\displaystyle {{1}\over{2}}$

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

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

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

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

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

    −3 Does not exist. 4 −12


Department of Mathematics
Last modified: 2025-09-29