Math 32B
Challenge Problem
Spring 2013
Calculus of Several Variables
June 8, 2013
1. The area of a circle
(2 pts)
A) Let r be a positive real number and let O = (0, 0) and P = (r, 0) be points in the
coordinate plane. Let be the (half)-line that emanates
Math 32B
More Practice Problems
Spring 2013
Calculus of Several Variables
The nal exam is around the corner and I will not be able to type the statements of all
the practice problems I had in mind. Therefore I am simply going to list some exercises from
t
Midterm 2 (practice problems) Spring 2013
Calculus of Several Variables
Math 32B
1. Circulation around a vortex
Let F be the vortex vector eld
F (x, y) =
y
x
+ 2
.
2
+y
x + y2
x2
Calculate
IR =
CR
F ds
where CR is the circle x2 + y 2 = R2 oriented counter
MATH 32 - GRAPHING POLYNOMIALS - EXAMPLE AND EXERCISES
Heres an example of the process of sketching a polynomial, followed by a few exercises,
supplemental to Homework 5.
1
Example: Lets sketch a graph of p(x) = x3 + 2x2 + 3x.
3
Well begin by nding the ze
MIDTERM
Math 32B
8/18/2010
Name:
Section:
Signature:
Read all of the following information before starting the exam:
Check your exam to make sure all pages are present.
NO CALCULATORS!
Show all work, clearly and in order, if you want to get full credit
Math 32B-4: Homework Week 10
1. Monday, March 7: Read Section 18.3 and do exercises 18.3.1, 18.3.3, 18.3.5, 18.3.7, 18.3.9,
18.3.11, 18.3.13, and 18.3.15.
2. Wednesday, March 9: Do exercises 18.3.18, 18.3.19, 18.3.20, 18.3.23, 18.3.25, 18.3.29, and
18.3.3