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

    4 −4 −2 2 Does not exist. 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 $\displaystyle \lim_{x\rightarrow 2}{f\left(x\right)}$.

    0 -2 Does not exist 2 1

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

    $\displaystyle {{1}\over{3}}$. $\displaystyle -{{1}\over{3}}$. Does not exist. $\displaystyle {{1}\over{18}}$. $\displaystyle -{{1}\over{18}}$.

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

    -1 0 Does not exist. 1

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

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

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

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

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

    0 −1. Does not exist. 1. −3.

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

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

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

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

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

    2 Does not exist. 1 0 −2 −1


Department of Mathematics
Last modified: 2025-10-06