# Calculus 3 : Partial Derivatives

## Example Questions

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### Example Question #1 : Partial Derivatives

Evaluate:

Does not exist

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.

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 #3 : Partial Derivatives

Calculate the following limit.

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

Does not exist

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.

Explanation:

Explanation:

Explanation:

Explanation:

Explanation: