1. Find $\displaystyle \lim_{x\rightarrow 0}{{{1-\cos x}\over{x^2}}}$.

    0 −2 $\displaystyle {{1}\over{2}}$ 2 1 $\displaystyle -{{1}\over{2}}$

  2. Find $\displaystyle \lim_{x\rightarrow 0}{{{e^{4\,x}-2\,e^{2\,x}+1}\over{x^2}}}$.

    4 $\displaystyle {{1}\over{4}}$ 1 0

  3. Find $\displaystyle\lim_{x\to 0+} \sqrt{x}\,\ln x $.

    1 $-\infty$ $\infty$ 0

  4. Find $\displaystyle \lim_{x\rightarrow 0}{{{3^{x}-7^{x}}\over{x}}}$.

    $\displaystyle \ln \left({{3}\over{7}}\right)$ 0 $\displaystyle {{1}\over{\ln \left({{3}\over{7}}\right)}}$ $\displaystyle {{1}\over{\ln \left({{7}\over{3}}\right)}}$ 1 $\displaystyle \ln \left({{7}\over{3}}\right)$

  5. Find $\displaystyle \lim_{x\rightarrow \infty }{\left({{2}\over{x}}+1\right)^{x}}$.

    $\displaystyle e^ {- 1 }$ 2 1 $\displaystyle e^2$ $\displaystyle e^ {- 2 }$ e


Department of Mathematics
Last modified: 2026-09-12