Generating...                               quiz03_n20

  1. Let $\displaystyle f(x) = \begin{cases} x^2-8\,x+18 & \mbox{ if } x \le 4 ; \\ 3\,x-8 & \mbox{ if } x > 4 . \end{cases} $

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

    Does not exist 0 -2 4 2

  2. Find $\displaystyle \lim_{x\rightarrow \sqrt{3}}{{{{{1}\over{x^2}}-{{1}\over{3}}}\over{ x^2-3}}}$.

    $\displaystyle {{1}\over{3}}$ $\displaystyle -{{1}\over{9}}$. $\displaystyle -{{1}\over{3}}$ $\displaystyle {{1}\over{9}}$. Does not exist.

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

    5 Does not exist. −5 $\displaystyle -{{5}\over{6}}$ $\displaystyle {{5}\over{6}}$

  4. Find $\displaystyle \lim_{x\rightarrow -3}{\left\vert x+3\right\vert }$.

    $-1$ 3 $1$ 0 Does not exist.

  5. 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.

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

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

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

    4 2 −2 −4 Does not exist. 0

  8. Find $\displaystyle \lim_{x\rightarrow 3}{{{x^2-5\,x+6}\over{x-3}}}$.

    3. 0 −1. Does not exist. 1.

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

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

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

    Does not exist. 0 2 −1 1 −2


Department of Mathematics
Last modified: 2025-09-14