Generating...                               quiz05_n24

Let

$\displaystyle f(x) = \begin{cases} 2\,x+4 & \mbox{ if } x \le -1 ; \\ -{{2}... ...}} & \mbox{ if } -1 < x < 0 ; \\ 2\,x^2+3 & \mbox{ if } x \ge 0 \end{cases}$

Then answer the following questions.

  1. $f(x)$ is

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

  2. $f(x)$ is

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

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

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

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

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

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

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


Department of Mathematics
Last modified: 2026-03-24