# Solutions to Problem Set 10

Math 311-01/02

2-9-2018

[Vector functions problems]

1. Find the value of if it exists.

Note that

So

2. Show that the following vector function has constant length:

Hence, .

3. Define by

Prove or disprove: f is continuous at .

Since , the function is not continuous at .

4. Let .

Compute and .

5. Let .

Compute and .

6. Find parametric equations for the tangent line to

The point of tangency is . Now

Thus, is a vector tangent to the curve, so it's parallel to the tangent line to the curve. The tangent line is

7. Compute the integral .

8. Compute the integral .

Happiness depends upon ourselves. - Aristotle

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