Generating...                               quiz03_n0

  1. Find $\displaystyle \lim_{x\rightarrow 0}{{{3-\sqrt{x+9}}\over{x\,\sqrt{x+1}}}}$.

    1. −1. $\displaystyle -{{1}\over{6}}$. $\displaystyle {{1}\over{6}}$. Does not exist.

  2. Find $\displaystyle \lim_{x\rightarrow -2}{{{x+2}\over{\left\vert x+2\right\vert }}}$.

    1 -1 Does not exist. 0

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

    4 −2 Does not exist. 0 2 −4

  4. If 5 $\le f(x) \le$ $\displaystyle x^2-4\,x+9$ for all $x$, find $\displaystyle \lim_{x\rightarrow 2}{f\left(x\right)}$.

    0 5. 2. Does not exist.

  5. Let $\displaystyle f(x) = \begin{cases} x^2-8\,x+15 & \mbox{ if } x \le 4 ; \\ 9-2\,x & \mbox{ if } x > 4 . \end{cases} $

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

    0 1 1 Does not exist -1

  6. Find $\displaystyle \lim_{x\rightarrow -2}{{{x^2+x-2}\over{x^2-2\,x-8}}}$.

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

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

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

  8. Find $\displaystyle \lim_{x\rightarrow -4}{\left\vert x+4\right\vert }$.

    $-1$ $1$ 4 Does not exist. 0

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

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

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

    Does not exist. 0 4.


Department of Mathematics
Last modified: 2025-06-19