Generating...                               quiz05_n29

Let

$\displaystyle f(x) = \begin{cases} x+7 & \mbox{ if } x \le -3 ; \\ -{{12}\over{x}} & \mbox{ if } -3 < x < 0 ; \\ x^2-2 & \mbox{ if } x \ge 0 \end{cases}$

Then answer the following questions.

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

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

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

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

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

    $-\infty$ Does not exist. 4 −4 $\infty$

  4. $f(x)$ is

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

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

    4 $\infty$ Does not exist. $-\infty$ −4


Department of Mathematics
Last modified: 2026-09-10