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

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

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

    Does not exist. 0 0 9

  4. Find $\displaystyle \lim_{x\rightarrow -2}{{{f\left(x\right)+5}\over{x+6}}}$.

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

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

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


Department of Mathematics
Last modified: 2026-08-20