Generating...                               quiz05_n5

Let

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

Then answer the following questions.

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

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

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

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

  3. $f(x)$ is

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

  4. $f(x)$ is

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

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

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


Department of Mathematics
Last modified: 2025-09-14