Generating...                               quiz17_n27

  1. Find $\displaystyle \lim_{x\rightarrow \infty }{\left(1-{{3}\over{x}}\right)^{x}}$.

    e $\displaystyle e^ {- 3 }$ $\displaystyle e^3$ $\displaystyle e^ {- 1 }$ −3 1

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

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

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

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

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

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

  5. Find $\displaystyle\lim_{x\to 0+} x^2\,\ln x $.

    1 0 $-\infty$ $\infty$


Department of Mathematics
Last modified: 2025-06-19