Let

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

Then answer the following questions.

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

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

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

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

  3. $f(x)$ is

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

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

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

  5. $f(x)$ is

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


Department of Mathematics
Last modified: 2026-10-12