Limits & Continuity

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These questions test conceptual understanding of limits and continuity, as well as ability to explicitly compute limits for basic functions.

[Limits] 1

Consider the function:

$f(x) = \left\{ \begin{array} {1 1} 2 & \quad \text{if x > 9} \\ 2 & \quad \text{if x = 9}\\ -x + 14 & \quad \text{if –7 \le x < 9} \\ 21 & \quad \text{if x < –7} \end{array} \right.$

A

$\text{lim}_{x \rightarrow 9^–} f(x) = 2$

B

$\text{lim}_{x \rightarrow 9^–} f(x) = 5$

C

$\text{lim}_{x \rightarrow 9^–} f(x) = 6$

D

$\text{lim}_{x \rightarrow 9^–} f(x) = 14$

E

$\text{lim}_{x \rightarrow 9^–} f(x) = 21$

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[Continuity] 1

A drippy faucet adds one milliliter to the volume of water in a tub at precisely one-second intervals. Let $f$ be the function that represents the volume of water in the tub at time $t$. Which of the following statements is correct?

A

$f$ is a continuous function at every time $t$

B

$f$ is continuous for all $t$ other than the precise instants when the water drips into the tub.

C

$f$ is not continuous at any time $t$.

D

There is not enough information to know where $f$ is continuous.

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