Generating...                               quiz05_n19

Let

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

Then answer the following questions.

  1. $f(x)$ is

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

  2. $f(x)$ is

    continuous at x = −2 . discontinuous at x = −2 .

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

    $\displaystyle \infty $ 3 −3 Does not exist. $\displaystyle -\infty $

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

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

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

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


Department of Mathematics
Last modified: 2026-07-16