Let

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

Then answer the following questions.

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

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

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

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

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

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

  4. $f(x)$ is

    continuous at x = −1 . discontinuous at x = −1 .

  5. $f(x)$ is

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


Department of Mathematics
Last modified: 2026-01-11