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

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

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

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

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

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

  4. If −3 $\le f(x) \le$ 3 for all $x$, find $\displaystyle \lim_{x\rightarrow 0}{x^2\,f\left(x\right)}$.

    Does not exist. 9. 0

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

    0 1 -1 Does not exist.

  6. Find $\displaystyle \lim_{x\rightarrow 0}{{{2-\sqrt{x+4}}\over{x\,\sqrt{x+9}}}}$.

    $\displaystyle {{1}\over{3}}$. $\displaystyle -{{1}\over{3}}$. $\displaystyle -{{1}\over{12}}$. Does not exist. $\displaystyle {{1}\over{12}}$.

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

    4. 0 3. Does not exist.

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

    Does not exist. 2. −2. 4. 0

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

    Does not exist. −3 3 $\displaystyle -{{1}\over{2}}$ $\displaystyle {{1}\over{2}}$

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

    −8 4 0 8 −4 Does not exist.


Department of Mathematics
Last modified: 2026-10-01