1. Find $\displaystyle \lim_{x\rightarrow {{\pi}\over{2}}}{\tan x}$.

    $\displaystyle \infty $ Does not exist. $\displaystyle {{\pi}\over{2}}$ $\displaystyle -\infty $ 0

  2. Find the vertical asymptotes for $y = \displaystyle {{-x^2-5\,x-6}\over{x^2-3\,x}} $ .

    x = 3 x = −3 and x = −2 x = 0 x = −3 x = 3 and x = 0 x = −2 No vertical asymptote

  3. Find $\displaystyle \lim_{x\rightarrow 3}{{{x^2+x-2}\over{x-3}}}$.

    3 $\displaystyle -\infty $ $\displaystyle \infty $ 0 Does not exist.

  4. Find $\displaystyle \lim_{x\rightarrow \infty }{{{x}\over{\sqrt{x^2+1}}}}$ .

    −1 Does not exist. 1 −1 0 1

  5. Find $\displaystyle\lim_{x\to {{\pi}\over{2}} \mbox{ + }} \tan x $ .

    0 $\displaystyle -\infty $ Does not exist. $\displaystyle {{\pi}\over{2}}$ $\displaystyle \infty $

  6. Find $\displaystyle -\lim_{x\rightarrow -2}{{{1}\over{x+2}}}$.

    $\infty$ 0 Does not exist. −2 $-\infty$

  7. Find $\displaystyle\lim_{x\to\infty} \left( \sqrt{9\,x^2+8\,x}-3\,x \right)$ .

    $\displaystyle {{4}\over{3}}$ 0 $\displaystyle -{{3}\over{4}}$ $\displaystyle -{{4}\over{3}}$ Does not exist. $\displaystyle {{3}\over{4}}$

  8. Find $\displaystyle\lim_{x\to -3 \mbox{ - }} -{{1}\over{x+3}} $ .

    $\displaystyle -\infty $ −3 $\displaystyle \infty $ Does not exist. 0

  9. Find the horizontal asymptotes for $y = \displaystyle {{x^2+{{5\,x}\over{2}}-6}\over{x^2+3\,x+2}} $ .

    No horizontal asymptote $\displaystyle y={{3}\over{2}}$ y = 1 and y = −1 $\displaystyle y={{3}\over{2}}$ and y = −4 y = 1 y = −1 y = −4

  10. Find $\displaystyle -\lim_{x\rightarrow -1}{{{1}\over{x^2+2\,x+1}}}$.

    −1. Does not exist. 0 $\displaystyle \infty $. $\displaystyle -\infty $. 1


Department of Mathematics
Last modified: 2025-10-16