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

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

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

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

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

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

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

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

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

    0 1 $\infty$


Department of Mathematics
Last modified: 2022-08-01