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

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

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

    1 $\infty$ 0

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

    $\infty$ 0 $-\infty$ 1

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

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

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

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


Department of Mathematics
Last modified: 2025-04-04