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