Generating...                               quiz03_n18

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

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

  2. Let $\displaystyle f(x) = \begin{cases} x^2-8\,x+15 & \mbox{ if } x \le 4 ; \\ 3\,x-15 & \mbox{ if } x > 4 . \end{cases} $

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

    -3 Does not exist 0 1 -1

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

    Does not exist. −3. −4. 0 4.

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

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

  5. Find $\displaystyle\lim_{x\to 0} x^3 \cos\left(\frac{1}{x}\right)$

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

  6. Find $\displaystyle \lim_{x\rightarrow 0}{{{\left(x-1\right)^2-1}\over{x}}}$.

    −1 Does not exist. 1 2 0 −2

  7. 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.

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

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

  9. Find $\displaystyle \lim_{x\rightarrow 0}{{{x^2-x}\over{x^2-5\,x}}}$.

    1 $\displaystyle -{{1}\over{5}}$ −1 $\displaystyle {{1}\over{5}}$ Does not exist.

  10. Find $\displaystyle \lim_{x\rightarrow 1}{{{x-1}\over{\left\vert x-1\right\vert }}}$.

    1 Does not exist. 0 -1


Department of Mathematics
Last modified: 2026-07-16