Callahan
5.2: 1, 2, 4, 6
7.3: 13, 16, 33
9.1: 31, 32

1)  Find the partial derivatives of the following functions:

a)  :

b)  :

c)  :

d)  :

e)  :

f)  :

2)

a)  Suppose .  Find and :

b)  Find a point at which .  At such a point a small change in leaves the value of virtually unchanged.

So, any point on the line:

Satisfies .  One example is, .

c)  Find a point at which a small increase in the x-value produces the same change in as would the same-sized decrease in the y-value.

In other words, find a point at which the rate of change of with respect to is the negative of the rate of change of with respect to .

So, any point on the line:

4)  The second partial derivatives of are the partial derivatives of and  .  Find the four second partial derivatives of the following functions:

a)  :

b)  :

c)  :

d)  :

e)  :

6)  Show that the function satisfies the partial differential equation:

To find :

To find :

To find :

So it is a solution!

7.3: 13, 16, 33

9.1: 31, 32

Converted by Mathematica      April 27, 2004