Let

$\displaystyle f(x) = \begin{cases} x+6 & \mbox{ if } x \le -3 ; \\ -{{12}\o... ...}} & \mbox{ if } -3 < x < 0 ; \\ 2\,x^2+1 & \mbox{ if } x \ge 0 \end{cases}$

Then answer the following questions.

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

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

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

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

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

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

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

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

  5. $f(x)$ is

    continuous at x = −3 . discontinuous at x = −3 .

  6. $f(x)$ is

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


Department of Mathematics
Last modified: 2026-02-02