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

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

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

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

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

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

  4. Find $\displaystyle \lim_{x\rightarrow 0}{{{\ln \cos x}\over{x^2}}}$.

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

  5. Find $\displaystyle \lim_{x\rightarrow 0}{{{x}\over{7^{x}-2^{x}}}}$.

    $\displaystyle {{1}\over{\ln \left({{7}\over{2}}\right)}}$ $\displaystyle \ln \left({{7}\over{2}}\right)$ 1 $\displaystyle {{1}\over{\ln \left({{2}\over{7}}\right)}}$ 0 $\displaystyle \ln \left({{2}\over{7}}\right)$


Department of Mathematics
Last modified: 2026-04-14