Generating...                               quiz03_n26

  1. Find $\displaystyle\lim_{x\to 0} x^4 \cos\left(\frac{1}{x}\right)$

    $1$ $-1$ Does not exist. 0

  2. If 4 $\le f(x) \le$ $\displaystyle x^2-2\,x+5$ for all $x$, find $\displaystyle \lim_{x\rightarrow 1}{f\left(x\right)}$.

    0 Does not exist. 1. 4.

  3. Find $\displaystyle \lim_{x\rightarrow 0}{{{\left(x+2\right)^2-4}\over{x}}}$.

    2 0 −2 −4 Does not exist. 4

  4. Find $\displaystyle \lim_{x\rightarrow -3}{{{x^2+x-6}\over{x^2-2\,x-15}}}$.

    5 −5 $\displaystyle {{5}\over{8}}$ Does not exist. $\displaystyle -{{5}\over{8}}$

  5. Find $\displaystyle \lim_{x\rightarrow 3}{{{x-3}\over{\left\vert x-3\right\vert }}}$.

    Does not exist. 0 -1 1

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

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

  7. Find $\displaystyle \lim_{x\rightarrow 0}{{{2-\sqrt{x+4}}\over{x\,\sqrt{x+4}}}}$.

    $\displaystyle -{{1}\over{8}}$. Does not exist. $\displaystyle {{1}\over{2}}$. $\displaystyle -{{1}\over{2}}$. $\displaystyle {{1}\over{8}}$.

  8. Let $\displaystyle f(x) = \begin{cases} x^2-8\,x+14 & \mbox{ if } x \le 4 ; \\ 8-2\,x & \mbox{ if } x > 4 . \end{cases} $

    Find $\displaystyle \lim_{x\rightarrow 4}{f\left(x\right)}$.

    -2 0 2 0 Does not exist

  9. If −1 $\le f(x) \le$ 1 for all $x$, find $\displaystyle \lim_{x\rightarrow 0}{x^2\,f\left(x\right)}$.

    0 1. Does not exist.

  10. Find $\displaystyle \lim_{x\rightarrow 1}{{{1-x}\over{1-\sqrt{x}}}}$.

    0 −2 Does not exist. −1 1 2


Department of Mathematics
Last modified: 2026-03-24