Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Divergence

Study concepts, example questions & explanations for Calculus 3

Create An Account

All Calculus 3 Resources

6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #14 : Line Integrals

Compute the divergence of the vector $\left \langle xy^2,y^3z,z^3y^2\right \rangle$ .

Possible Answers:

y^2+3y^2z+3y^2z^2

y^2z+xyz

y^2+4xy+z^3

xy+3yz+3xy^2

Correct answer:

y^2+3y^2z+3y^2z^2

Explanation:

To find the divergence of the vector

$v=\left \langle a,b,c\right \rangle$ ,

we use the formula

$div(v)=\frac{\partial a}{\partial x}+\frac{\partial b}{\partial y}+\frac{\partial c}{\partial z}$ .

Computing each partial derivative, we get

$\frac{\partial }{\partial x}(xy^2)=y^2, \frac{\partial }{\partial y}(y^3z)=3y^2z,\frac{\partial }{\partial z}(y^2z^3)=3y^2z^2$ .

Adding them up gives us the correct answer.

Report an Error

Example Question #15 : Line Integrals

Compute the divergence of the vector $\left \langle x^2y,xy^2z,x^4z^3\right \rangle$ .

Possible Answers:

2xyz+3x^2y+4x^3z^3

2xy+2xyz+4x^4z^3

2xy+2xyz+3x^4z^2

3x^2y+4xyz+yz^3

Correct answer:

2xy+2xyz+3x^4z^2

Explanation:

To find the divergence of the vector $v=\left \langle a,b,c\right \rangle$ , we use the formula

$div(v)=\frac{\partial a}{\partial x}+\frac{\partial b}{\partial y}+\frac{\partial c}{\partial z}$ .

Computing each partial derivative, we get

$\frac{\partial }{\partial x}(x^2y)=2xy, \frac{\partial }{\partial y}(xy^2z)=2xyz,\frac{\partial }{\partial z}(x^4z^3)=3x^4z^2$ .

Adding them up gives us the correct answer.

Report an Error

Example Question #16 : Line Integrals

Compute the divergence of the vector.

$\left \langle yz,x^6y,z^5\right \rangle$

Possible Answers:

x^6+5z^4

x^7+4z^4

y+x^5+4z^3

y+5x^4

Correct answer:

x^6+5z^4

Explanation:

To find the divergence of the vector $v=\left \langle a,b,c\right \rangle$ , we use the formula

$div(v)=\frac{\partial a}{\partial x}+\frac{\partial b}{\partial y}+\frac{\partial c}{\partial z}$ .

Computing each partial derivative, we get

$\frac{\partial }{\partial x}(yz)=0, \frac{\partial }{\partial y}(x^6y)=x^6,\frac{\partial }{\partial z}(z^5)=5z^4$ .

Adding them up gives us the correct answer.

Report an Error

Example Question #11 : Line Integrals

Find the divergence of the vector $\left \langle 2x^3yz,3y^3,z^8\right \rangle$

Possible Answers:

6x^2yz+9y^2+8z^7

$\left \langle 6x^2yz,9y^2,8z^7\right \rangle$

x^6yz+4y^3+z^8

5x^2yz+y^4+8z^7

Correct answer:

6x^2yz+9y^2+8z^7

Explanation:

The formula for the divergence of a vector $a=\left \langle A,B,C\right \rangle$ is $div(a)=\frac{\partial A}{\partial x}+\frac{\partial B}{\partial y}+\frac{\partial C}{\partial z}$ . Using the vector from the problem statement, we get $\frac{\partial }{\partial x}(2x^3yz)=6x^2yz, \frac{\partial }{\partial y}(3y^3)=9y^2,\frac{\partial }{\partial z}(z^8)=8z^7$ . Adding them up gets us the correct answer.

Report an Error

Example Question #21 : Line Integrals

Find the divergence of the vector $\left \langle x^2y^2z^2,3y^5,17z\right \rangle$

Possible Answers:

xy^2z^2+y^5+z

x^2y^2z^2+15y^5-17z

3xyz+3y^5-17z

2xy^2z^2+15y^4+17

Correct answer:

2xy^2z^2+15y^4+17

Explanation:

To find the divergence a vector $a=\left \langle A,B,C\right \rangle$ , you use the following definition: $div(a)=\frac{\partial A}{\partial x}+\frac{\partial B}{\partial y}+\frac{\partial C}{\partial z}$ . Applying this to the vector from the problem statement, we get $\frac{\partial A}{\partial x}=2xy^2z^2, \frac{\partial B}{\partial y}=15y^4,\frac{\partial C}{\partial z}=17$ . Adding all of these up, according to the definition, will produce the correct answer.

Report an Error

Example Question #22 : Line Integrals

Find the divergence of the following vector: $\left \langle yz^3,xy^5z,3xz\right \rangle$

Possible Answers:

$\left \langle 0,5xy^4z,3x\right \rangle$

$\left \langle 0,5xy^4z,3\right \rangle$

$\left \langle 3yz^2,y^5z,3x\right \rangle$

$\left \langle 3yz^2,5xy^3z,3z\right \rangle$

Correct answer:

$\left \langle 0,5xy^4z,3x\right \rangle$

Explanation:

To find the divergence a vector $a=\left \langle A,B,C\right \rangle$ , you use the following definition: $div(a)=\frac{\partial A}{\partial x}+\frac{\partial B}{\partial y}+\frac{\partial C}{\partial z}$ . Applying this to the vector from the problem statement, we get $\frac{\partial A}{\partial x}=0, \frac{\partial B}{\partial y}=5xy^4z,\frac{\partial C}{\partial z}=3x$ . Adding all of these up, according to the definition, will produce the correct answer.

Report an Error

Example Question #23 : Line Integrals

Find the divergence of the vector $\left \langle \cos(x),-2\sin(y),x^2y^2z^2\right \rangle$

Possible Answers:

$\left \langle -\sin(x),-2\cos(y),2x^2y^2z\right \rangle$

$\left \langle \sin(x),\cos(y),x^2y^2\right \rangle$

$\left \langle -\sin(x),2\cos(y),2x^2y^2z\right \rangle$

$\left \langle \sin(x),-2\cos(y),x^2y^2z\right \rangle$

Correct answer:

$\left \langle -\sin(x),-2\cos(y),2x^2y^2z\right \rangle$

Explanation:

To find the divergence a vector $a=\left \langle A,B,C\right \rangle$ , you use the following definition: $div(a)=\frac{\partial A}{\partial x}+\frac{\partial B}{\partial y}+\frac{\partial C}{\partial z}$ . Applying this to the vector from the problem statement, we get $\frac{\partial A}{\partial x}=-\sin(x), \frac{\partial B}{\partial y}=-2\cos(x),\frac{\partial C}{\partial z}=2x^2y^2z$ . Adding all of these up, according to the definition, will produce the correct answer.

Report an Error

Example Question #22 : Line Integrals

Find the divergence of the vector $\left \langle 2x,6x^2y^3,z^4\right \rangle$

Possible Answers:

2+18xy^2+4z^3

2+6xy^3+z^5

18x^2y^3+4z^3

2+18x^2y^2+4z^3

Correct answer:

2+18x^2y^2+4z^3

Explanation:

To find the divergence of a vector $v=\left \langle A,B,C\right \rangle$ , we apply the following definition: $div(v)=\frac{\partial A}{\partial x}+\frac{\partial B}{\partial y}+\frac{\partial C}{\partial z}$ . Applying the definition to the vector from the problem statement, we get $\frac{\partial }{\partial x}(2x)+\frac{\partial }{\partial y}(6x^2y^3)+\frac{\partial }{\partial z}(z^4)=2+18x^2y^2+4z^3$

Report an Error

Example Question #21 : Line Integrals

Find the divergence of the vector $\left \langle xz^4,6x^5y,x^4yz^2\right \rangle$

Possible Answers:

z^4+6x^5+2x^4yz

z^4+5x^4+2x^3yz^2

z^4+30x^6+8x^3yz

z^4+6x^5+x^4y

Correct answer:

z^4+6x^5+2x^4yz

Explanation:

To find the divergence of a vector $v=\left \langle A,B,C\right \rangle$ , we apply the following definition: $div(v)=\frac{\partial A}{\partial x}+\frac{\partial B}{\partial y}+\frac{\partial C}{\partial z}$ . Applying the definition to the vector from the problem statement, we get $\frac{\partial }{\partial x}(xz^4)+\frac{\partial }{\partial y}(6x^5y)+\frac{\partial }{\partial z}(x^4yz^2)=z^4+6x^5+2x^4yz$

Report an Error

Example Question #21 : Line Integrals

Find the divergence of the vector $\left \langle 12x^2y,4y^2z,xy^5\right \rangle$

Possible Answers:

24xy+8yz

12x+8y

3xy+2yz+z

12x+4xyz

Correct answer:

24xy+8yz

Explanation:

To find the divergence of a vector $v=\left \langle A,B,C\right \rangle$ , we apply the following definition: $div(v)=\frac{\partial A}{\partial x}+\frac{\partial B}{\partial y}+\frac{\partial C}{\partial z}$ . Applying the definition to the vector from the problem statement, we get $\frac{\partial }{\partial x}(12x^2y)+\frac{\partial }{\partial y}(4y^2z)+\frac{\partial }{\partial z}(xy^5)=24xy+8yz$

Report an Error

View Calculus 3 Tutors

Thomas
Certified Tutor

Dartmouth College, Bachelor in Arts, Biochemistry and Molecular Biology. Columbia University in the City of New York, Master ...

View Calculus 3 Tutors

Hannah
Certified Tutor

University of Florida, Bachelor of Science, Mathematics.

View Calculus 3 Tutors

Shangren
Certified Tutor

Rochester Institute of Technology, Bachelor of Science, Chemical Engineering. Rensselaer Polytechnic Institute, Doctor of Phi...

All Calculus 3 Resources

6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Miami, SSAT Tutors in Houston, English Tutors in Philadelphia, SAT Tutors in Chicago, Computer Science Tutors in Seattle, LSAT Tutors in Dallas Fort Worth, Statistics Tutors in Houston, GRE Tutors in Washington DC, Chemistry Tutors in San Francisco-Bay Area, Spanish Tutors in Philadelphia

Popular Courses & Classes

Spanish Courses & Classes in Philadelphia, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in Phoenix, GMAT Courses & Classes in Houston, LSAT Courses & Classes in Phoenix, SSAT Courses & Classes in Chicago, SSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Seattle, ACT Courses & Classes in Atlanta, ISEE Courses & Classes in Washington DC

Popular Test Prep

ACT Test Prep in Atlanta, SSAT Test Prep in Phoenix, SSAT Test Prep in Atlanta, MCAT Test Prep in Denver, SSAT Test Prep in Chicago, SSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Seattle, MCAT Test Prep in Chicago, MCAT Test Prep in Houston, ISEE Test Prep in Houston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Calculus 3 : Divergence

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #14 : Line Integrals

Example Question #15 : Line Integrals

Example Question #16 : Line Integrals

Example Question #11 : Line Integrals

Example Question #21 : Line Integrals

Example Question #22 : Line Integrals

Example Question #23 : Line Integrals

Example Question #22 : Line Integrals

Example Question #21 : Line Integrals

Example Question #21 : Line Integrals

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: