Generating...                               quiz06_n25

  1. Find $\displaystyle\lim_{x\to 4 \mbox{ + }} {{-x^2-x+2}\over{x-4}} $ .

    $\displaystyle \infty $ $\displaystyle -\infty $ 0 4 Does not exist.

  2. Find $\displaystyle \lim_{x\rightarrow 4}{{{x^2+x-6}\over{x-4}}}$.

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

  3. Find $\displaystyle \lim_{x\rightarrow -\infty }{{{x}\over{\sqrt{4\,x^2+9}}}}$ .

    $\displaystyle {{1}\over{2}}$ $\displaystyle {{1}\over{3}}$ Does not exist. $\displaystyle -{{1}\over{2}}$ $\displaystyle -{{1}\over{3}}$ 0

  4. Find $\displaystyle \lim_{x\rightarrow -3}{{{1}\over{x+3}}}$.

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

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

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

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

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

  7. Find the horizontal asymptotes for $y = \displaystyle {{2\,x^2-9\,x+4}\over{x^2-4\,x+4}} $ .

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

  8. Find $\displaystyle\lim_{x\to\infty} \left( {{1}\over{\sqrt{x^2+4\,x}-x}} \right)$ .

    −2 0 Does not exist. $\displaystyle {{1}\over{2}}$ $\displaystyle -{{1}\over{2}}$ 2

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

    4 Does not exist. −4 $\displaystyle -{{1}\over{4}}$ $\displaystyle {{1}\over{4}}$

  10. Find $\displaystyle\lim_{x\to \mbox{ } \infty} {{1000}\over{x+1000}}$

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


Department of Mathematics
Last modified: 2026-10-30