Calculus 3 : Partial Derivatives

Study concepts, example questions & explanations for Calculus 3

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Example Questions

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Example Question #1 : Partial Derivatives

Evaluate:

Possible Answers:

Does not exist

Correct answer:

Explanation:

Since we won't have any divided by zero problems, we can just evaluate at the point.

Example Question #2 : Partial Derivatives

Calculate the following limit.

Possible Answers:

Correct answer:

Explanation:

We can calculate the limit

by simply plugging in  because the value is defined at  and around that point.

So we get

.

Example Question #1 : Partial Derivatives

Calculate the following limit.

Possible Answers:

Correct answer:

Explanation:

We can calculate the limit

by simply plugging in  because the value is defined at  and at every value in .

So we get

.

Example Question #4 : Partial Derivatives

Evaluate 

Possible Answers:

None of the other answers

Does not exist

Correct answer:

Does not exist

Explanation:

If we try evaluating the limit along two different paths, , we have

And

Since evaluating along these two paths yielded diffferent values, the limit does not exist.

Example Question #5 : Partial Derivatives

Possible Answers:

Correct answer:

Explanation:

Example Question #6 : Partial Derivatives

Possible Answers:

Correct answer:

Explanation:

Example Question #2 : Partial Derivatives

Possible Answers:

Correct answer:

Explanation:

Example Question #8 : Partial Derivatives

Possible Answers:

Correct answer:

Explanation:

Example Question #9 : Partial Derivatives

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Partial Derivatives

Possible Answers:

Correct answer:

Explanation:

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