Generating...                               quiz05_n1

Let

$\displaystyle f(x) = \begin{cases} -2\,x-7 & \mbox{ if } x \le -3 ; \\ -{{3... ...{x}} & \mbox{ if } -3 < x < 0 ; \\ -x^2-2 & \mbox{ if } x \ge 0 \end{cases}$

Then answer the following questions.

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

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

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

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

  3. $f(x)$ is

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

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

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

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

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


Department of Mathematics
Last modified: 2025-10-30