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

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

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

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

  3. Find $\displaystyle\lim_{x\to 0+} x^{x^2} $.

    1 0 $\infty$

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

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

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

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


Department of Mathematics
Last modified: 2025-07-29