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

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

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

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

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

    $\infty$ 0 1 $-\infty$

  4. Find $\displaystyle \lim_{x\rightarrow 0}{{{6^{x}-3^{x}}\over{x}}}$.

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

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

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


Department of Mathematics
Last modified: 2025-09-12