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

    $1$ Does not exist. $-1$ 2 0

  2. Let $\displaystyle f(x) = \begin{cases} x^2-4\,x+6 & \mbox{ if } x \le 2 ; \\ 4-x & \mbox{ if } x > 2 . \end{cases} $

    Find $\displaystyle \lim_{x\rightarrow 2}{f\left(x\right)}$.

    1 Does not exist -2 0 2

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

    −2 2 0 4 Does not exist. −4

  4. If 4 $\le f(x) \le$ $\displaystyle x^2-6\,x+13$ for all $x$, find $\displaystyle \lim_{x\rightarrow 3}{f\left(x\right)}$.

    Does not exist. 3. 4. 0

  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 $\displaystyle \lim_{x\rightarrow 4}{{{x-4}\over{\left\vert x-4\right\vert }}}$.

    1 Does not exist. 0 -1

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

    Does not exist. 0 −1. −3. 1.

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

    $\displaystyle {{4}\over{5}}$ 4 Does not exist. $\displaystyle -{{4}\over{5}}$ −4

  9. Find $\displaystyle \lim_{x\rightarrow 0}{{{\left(x-4\right)^2-16}\over{x}}}$.

    −8 8 4 Does not exist. 0 −4

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

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


Department of Mathematics
Last modified: 2025-03-29