Calculus 3 : Divergence

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #11 : Line Integrals

Compute the divergence of the vector .

Possible Answers:

Correct answer:

Explanation:

To find the divergence of the vector 

,

we use the formula 

.

Computing each partial derivative, we get 

.

Adding them up gives us the correct answer.

Example Question #12 : Line Integrals

Compute the divergence of the vector .

Possible Answers:

Correct answer:

Explanation:

To find the divergence of the vector , we use the formula 

.

Computing each partial derivative, we get 

.

Adding them up gives us the correct answer.

Example Question #13 : Line Integrals

Compute the divergence of the vector. 

Possible Answers:

Correct answer:

Explanation:

To find the divergence of the vector , we use the formula 

.

Computing each partial derivative, we get 

.

Adding them up gives us the correct answer.

Example Question #14 : Line Integrals

Find the divergence of the vector 

Possible Answers:

Correct answer:

Explanation:

The formula for the divergence of a vector  is . Using the vector from the problem statement, we get . Adding them up gets us the correct answer.

Example Question #21 : Line Integrals

Find the divergence of the vector 

Possible Answers:

Correct answer:

Explanation:

To find the divergence a vector , you use the following definition: . Applying this to the vector from the problem statement, we get . Adding all of these up, according to the definition, will produce the correct answer.

Example Question #22 : Line Integrals

Find the divergence of the following vector: 

Possible Answers:

Correct answer:

Explanation:

To find the divergence a vector , you use the following definition: . Applying this to the vector from the problem statement, we get . Adding all of these up, according to the definition, will produce the correct answer.

Example Question #23 : Line Integrals

Find the divergence of the vector 

Possible Answers:

Correct answer:

Explanation:

To find the divergence a vector , you use the following definition: . Applying this to the vector from the problem statement, we get . Adding all of these up, according to the definition, will produce the correct answer.

Example Question #24 : Line Integrals

Find the divergence of the vector 

Possible Answers:

Correct answer:

Explanation:

To find the divergence of a vector , we apply the following definition: . Applying the definition to the vector from the problem statement, we get 

Example Question #25 : Line Integrals

Find the divergence of the vector 

Possible Answers:

Correct answer:

Explanation:

To find the divergence of a vector , we apply the following definition: . Applying the definition to the vector from the problem statement, we get 

Example Question #26 : Line Integrals

Find the divergence of the vector 

Possible Answers:

Correct answer:

Explanation:

To find the divergence of a vector , we apply the following definition: . Applying the definition to the vector from the problem statement, we get 

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