Multiple choice

Which one of the following functions is strictly bounded?

  1. $\frac{1}{x^2}$

  2. ex

  3. x2
  4. $e^{-x^2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\text{We have} \hspace{1cm} lim_{x \rightarrow 0} \frac{1}{x^2} = \infty \\ \hspace{2.7cm} lim_{x \rightarrow \infty} x^2 = \infty \\ \hspace{2.7cm} lim_{x \rightarrow \infty} e^{-x} = \infty \\ \hspace{2.7cm} lim_{x \rightarrow \infty} e^{-x^2} = 0 \\ \hspace{2.7cm} lim_{x \rightarrow 0} e^{-x^2} = 1 \hspace{1cm} \text{Thus $e^{-x^2}$ is strictly bounded.}$

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