Let

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

Then answer the following questions.

  1. $f(x)$ is

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

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

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

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

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

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

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

  5. $f(x)$ is

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


Department of Mathematics
Last modified: 2026-03-27