# Limits & Continuity

Lead Author(s): **Kelly Cline**

Student Price: **FREE**

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

Consider the function:

[math] 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.[/math]

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

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

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

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

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

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?

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

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

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

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