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

    0 $\infty$ 1

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

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

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

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

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

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

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

    $\infty$ $-\infty$ 1 0


Department of Mathematics
Last modified: 2026-08-04