Let

$\displaystyle f(x) = \begin{cases} x+8 & \mbox{ if } x \le -3 ; \\ -{{6}\ov... ...} & \mbox{ if } -3 < x < 0 ; \\ -2\,x^2-3 & \mbox{ if } x \ge 0 \end{cases}$

Then answer the following questions.

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

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

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

    −5 Does not exist. $-\infty$ 5 $\infty$

  3. $f(x)$ is

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

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

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

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

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


Department of Mathematics
Last modified: 2025-03-03