# Solutions to Problem Set 18

Math 311-01/02

2-27-2018

[Tangent plane problems]

1. Find the equation of the tangent plane and the equation of the normal line to

and gives . The point is .

At ,

The normal vector is

The normal line is

The tangent plane is

2. Find the equation of the tangent plane and the equation of the normal line to

and gives . The point is .

At ,

The normal vector is

The normal line is

The tangent plane is

3. (a) Find the equation of the tangent plane to

(b) Use the equation of the tangent plane to approximate z when .

(a) and gives . The point is .

At ,

The normal vector is

The tangent plane is

(b) Set and in the tangent plane equation and solve for z:

4. Find the equation of the tangent plane to

gives

The point is .

At ,

The normal vector is

The tangent plane is

5. Find the equation of the tangent plane to

gives

The point is .

At ,

The normal vector is

The tangent plane is

Love truth, but pardon error. - Voltaire

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