Math E-21a Fall 2013 HW #8 problems
Read sections 11.8 and 12.1 (and maybe 12.2-12.3) and do the following problems:
Problems to turn in on Thurs, Oct 31:
1. (Prob. 11.8/16) Use the Method of Lagrange Multipliers to find the maximum and minimum values of

Math E-21a Fall 2013 HW #11 problems
Problems due Thurs, Nov 21:
Section 12.9:
16. Evaluate the integral
R
(4 x 8 y ) dA , where R is the parallelogram with vertices (1,3) , (1, 3) , (3, 1) ,
and (1,5) . Use the coordinate transformation cfw_x 14 (u v), y

Math E-21a Fall 2013 HW #13 problems
Problems keyed to the 4th Edition
To be turned in Thurs, Dec 12:
Section 12.6:
2. Find the area of the part of the plane 2 x 5 y + z =
10 that lies above the triangle with vertices (0, 0) , (0, 6) ,
and (4, 0) .
4. Fin

Math E-21a Fall 2013 HW #7 problems
Problems to turn in on Thurs, Oct 24:
Section 11.7:
In problems 6-14, find the local maximum and minimum values and saddle point(s) of the function.
6. f ( x, y ) x 3 y 12 x 2 8 y
10. f ( x, y ) xy 1x 1y
12. f ( x, y )

Math E-21a Fall 2013 HW #14 problems
Do these problems, but dont turn them in:
Section 13.7:
In problem 10, use Stokes Theorem to evaluate
C
F dr . The curve C is oriented counterclockwise as viewed
from above, i.e. from the positive z-axis.
10. F( x, y,

Math E-21a Fall 2013 HW #9 problems
Problems to turn in on Thurs, Nov 7:
Section 12.2:
1
1
0
0
12. Calculate the iterated integral:
20. Calculate the double integral:
R
xy x 2 y 2 dx dy
x dA, R [0,1] [0,1] ( x, y ) : 0 x 1, 0 y 1
1 xy
Section 12.3:
y
dA

Math E-21a Fall 2013 HW #3 problems
Problems keyed to the 4th Edition
Problems to turn in on Thurs, Sept 26:
Section 9.6:
11. Sketch the graph of the function f ( x, y ) 6 3x 2 y .
12. Sketch the graph of the function f ( x, y ) cos x .
34. Find an equati

Math E-21a Fall 2013 HW #5 problems
Problems to turn in on Thurs, Oct 10:
Section 11.1:
20. Draw a contour map of the function f ( x, y ) x 3 y showing several level curves.
27. Sketch both a contour map and a graph of the function f ( x, y ) x 2 9 y 2 an

Math E-21a Fall 2013 HW #4 problems
Problems to turn in on Thurs, Oct 3:
Note: Bold indicates vector quantities.
Section 10.2:
16. Find the unit tangent vector T(t ) at the point with the value of the parameter t 1 where the position vector
is given by r

Math E-21a Fall 2013 HW #12 problems
Problems keyed to the 4th Edition
Problems due Thurs, Dec 5:
Section 13.4:
4. Evaluate the line integral by two methods: (a) directly and (b) using Greens Theorem.
x dx + y dy , C consists of the line segments from (0

Math E-21a Fall 2013 HW #6 problems
Problems to turn in on Thurs, Oct 17:
Section 11.3:
z
z
and
: sin( xyz ) x 2 y 3 z
48. Use implicit differentiation to find
x
y
xy
(That is, find vxx , vxy , v yx , and v yy .)
54. Find all the second partial derivative

Math E-21a Fall 2013 HW #2 problems
Problems keyed to the 4th Edition
Problems to turn in on Thurs, Sept 19:
Basic Concept Problems:
(a) Prove the Pythagorean Theorem. [Hint: This can be done, for example, by considering the areas of plane
figures like sq

Math E-21a Fall 2013 HW #10 problems
Problems to turn in on Thurs, Nov 14:
Section 12.7:
12. Evaluate the triple integral y dV where E is bounded by the planes x 0 , y 0 , z 0 , and
E
2x 2 y z 4 .
16. Evaluate the triple integral
T
xyz dV where T is the s

Math E-21a Fall 2013 HW #1 problems
Note: Points will be typically denoted using ordinary parentheses ( ), vectors using angled brackets
.
Due in class on Thurs, Sept 12:
Section 9.1:
8. Find the distance from (3, 7,5) to each of the following.
(a) The xy