 
Summary: MAT 307 FALL 2011 MIDTERM I EXAM
Name: ID Number:
Problem 1 2 3 4 5 6 Total
Score
Directions: Each problem is 15 points; some problems are easier, some harder. Do all of your
work on these pages and cross out any work that should be ignored. Use the backs of pages if
needed, indicating where you've done this. Notes, books, calculators and discussions with others
are not permitted.
1. Compute the gradient f of the function f(x, y) = xy, and sketch the gradient vector field.
1
2. Consider the functions
f(u, v) = (u + v, u  v, u2
 v2
), g(x, y, z) = x2
+ y2
 z2
.
Find the derivatives of f, g and of the composition g f.
2
3. The equation
