Generating...                               quiz06_n4

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

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

  2. Find $\displaystyle\lim_{x\to\infty} \left( {{1}\over{\sqrt{4\,x^2+7\,x}-2\,x}} \right)$ .

    $\displaystyle {{7}\over{4}}$ $\displaystyle -{{4}\over{7}}$ 0 $\displaystyle {{4}\over{7}}$ $\displaystyle -{{7}\over{4}}$ Does not exist.

  3. Find $\displaystyle\lim_{x\to 4 \mbox{ - }} {{-x^2-4\,x-3}\over{x-4}} $ .

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

  4. Find $\displaystyle \lim_{x\rightarrow \infty }{{{3\,x^3+5\,x^2-x}\over{-5\,x^3+3\,x^2+ 2}}}$.

    $\displaystyle {{3}\over{5}}$ $\displaystyle {{5}\over{3}}$ $\displaystyle -{{5}\over{3}}$ $\displaystyle -{{3}\over{5}}$ Does not exist.

  5. Find the vertical asymptotes for $y = \displaystyle {{x^2+7\,x+12}\over{x^2-9\,x+18}} $ .

    x = −3 and x = −4 x = 6 x = 3 and x = 6 No vertical asymptote x = 3 x = −4 x = −3

  6. Find $\displaystyle \lim_{x\rightarrow -2}{{{1}\over{x^2+4\,x+4}}}$.

    $\displaystyle {{1}\over{4}}$ −2. $\displaystyle \infty $. 0 $\displaystyle -\infty $. Does not exist.

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

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

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

    0 −1 1 1 −1 Does not exist.

  9. Find $\displaystyle\lim_{x\to {{\pi}\over{2}} \mbox{ - }} \sec x $ .

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

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

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


Department of Mathematics
Last modified: 2026-05-20