Limits & Continuity
Limits & Continuity

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.

[Limits] 1

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]

A

limx9f(x)=2\text{lim}_{x \rightarrow 9^–} f(x) = 2

B

limx9f(x)=5\text{lim}_{x \rightarrow 9^–} f(x) = 5

C

limx9f(x)=6\text{lim}_{x \rightarrow 9^–} f(x) = 6

D

limx9f(x)=14\text{lim}_{x \rightarrow 9^–} f(x) = 14

E

limx9f(x)=21\text{lim}_{x \rightarrow 9^–} f(x) = 21

Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
[Continuity] 1

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

A

ff is a continuous function at every time tt

B

ff is continuous for all tt other than the precise instants when the water drips into the tub.

C

ff is not continuous at any time tt.

D

There is not enough information to know where ff is continuous.

Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.
Locked Content
This Content is Locked
Only a limited preview of this text is available. You'll need to sign up to Top Hat, and be a verified professor to have full access to view and teach with the content.