Generating...                               quiz05_n18

Let

$\displaystyle f(x) = \begin{cases} x+2 & \mbox{ if } x \le -3 ; \\ {{6}\over{x}} & \mbox{ if } -3 < x < 0 ; \\ -x^2-2 & \mbox{ if } x \ge 0 \end{cases}$

Then answer the following questions.

  1. Find $\displaystyle\lim_{x\to -3 -} f(x)$.

    Does not exist. $-\infty$ $\infty$ −1 1

  2. Find $\displaystyle\lim_{x\to 0-} f(x)$.

    Does not exist. −2 $\displaystyle \infty $ $\displaystyle -\infty $ 2

  3. $f(x)$ is

    continuous from the left at $x = 0$ . continuous from the right at $x = 0$ . continuous from neither the left nor the right at $x = 0$ .

  4. Find $\displaystyle\lim_{x\to 0+} f(x)$.

    −2 $\displaystyle -\infty $ Does not exist. $\displaystyle \infty $ 2

  5. Find $\displaystyle\lim_{x\to -3 +} f(x)$.

    $\infty$ 2 $-\infty$ Does not exist. −2


Department of Mathematics
Last modified: 2026-10-28