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

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

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

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

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

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

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

    16 9 4 −3

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

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


Department of Mathematics
Last modified: 2025-07-05