Monday April 10

1.

a.

b.

Sec. 19.7:

Solve, write up and turn in:

Sec. 19.7:

Sec. 19.10:

1.

f(x,y)=the integral from 0 to x of sin(t^3y^2) dt

2.

fxx/2 x^2 +fxy x y +fyy/2 y^2 equals

A^2/(2fxx) +D/(2 fxx) y^2

where D is the discriminant and A=fxx x+fxy y.

Solve, write up and turn in:

Sec. 19.10:

__Friday April 14__

Check
out the **Exteme
Value Theorem and examples.****
Solve,
write up and turn in:
1. **Consider the function
f(x,y,z)=x^2+y^2-xz on the
domain

x

Sketch the domain and find the absolute maximum and minimum of the function.

**2. **Consider the
function f(x,y)=1+square root of (4x^2+y^2) on the
domain x^2+y^2__<__1.

Sketch the graph of the function
and name this surface.

Find the absolute minimum and maximum of
this function on the stated domain.

Explain why absolute extrema
necessarily exist for this function on this domain.

Change: problem 4b page 701 became a bonus problem worth extra 5 points; you can turn it in now,

or on April 24.