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

    −2 2 0 −4 Does not exist. 4

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

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

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

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

  4. Find $\displaystyle \lim_{x\rightarrow 16}{{{16-x}\over{4-\sqrt{x}}}}$.

    −8 −4 4 0 Does not exist. 8

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

    Does not exist. 1 0 -1

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

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

  7. Find $\displaystyle \lim_{x\rightarrow 4}{{{x^2-6\,x+8}\over{x-4}}}$.

    4. 0 Does not exist. 2. −2.

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

    $\displaystyle -{{1}\over{16}}$. $\displaystyle {{1}\over{16}}$. $\displaystyle -{{1}\over{4}}$ Does not exist. $\displaystyle {{1}\over{4}}$

  9. Let $\displaystyle f(x) = \begin{cases} x^2-4\,x+6 & \mbox{ if } x \le 2 ; \\ 3\,x-4 & \mbox{ if } x > 2 . \end{cases} $

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

    Does not exist 0 -2 5 2

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

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

  11. 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. 4. 0

  12. If −1 $\le f(x) \le$ $\displaystyle x^2-4\,x+3$ for all $x$, find $\displaystyle \lim_{x\rightarrow 2}{f\left(x\right)}$.

    −1. Does not exist. 2. 0


Department of Mathematics
Last modified: 2026-03-21