Math 233
Practice Final 3
Spring 2006
1. a) Find the equation of the plane containing the points P (1, 3, 0), Q(2, 1, 2) and R(0, 0, 1).
b) Find all points of intersection of the parametric curve r(t) = 2t2 2, t, 1 t t2 and the plane
x + y + z = 3.
2. Fin
Math 233
Practice Final 2
Spring 2006
1.Consider the function f (x, y ) = xexy . Let P be the point (1, 0).
(a) Find the rate of change of the function f at the point P in the direction of the point (3, 2).
(b) Give a direction in terms of a unit vector (
Math 233
Practice Final 1
Spring 2006
1) Express the double integral
x2 y x dA
R
as an interated integral and evaluate it, where R is the rst quadrant region enclosed by the curves
y = 0, y = x2 and y = 2 x. b) Find an equivalent iterated integral express
1. (15 points) Let f (x, y ) be a dierentiable function with the following
values of the partial derivatives fx (x, y ) and fy (x, y ) at certain points (x, y ):
x
0
2
1
y
0
1
2
fx (x, y ) fy (x, y )
3
2
2
5
1
4
(You are given more values than you will ne
Math 233
Practice Exam 2
Fall 2005
1. Find the critical points of f (x, y ) = x3 + y 2 + 2xy 4x 3y + 5 and classify each
as a relative maximum, relative minimum or saddle point.
2. An open (no top) rectangular box must have a volume of 6 cubic feet. Find
Math 233
Practice Exam 1
Spring 2006
1. (a) Consider the line L through points A = (2, 1, 1) and B = (5, 3, 2). Find the
intersection of the line L and the plane given by 2x 3y + 4z = 13.
(b) Find the distance of the point (2, 1, 1) and the plane given by
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
MATH 233
EXAM 1
Fall 2010
Spire ID:
NAME:
Section Number:
Instructors Name:
In this exam there are seven pages, including this one, and six problems . Make sure you
have them all before
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
MATH 233
FINAL EXAM
NAME:
Spring 2006
Student ID#
Section Number:
Instructors Name:
In problems that require reasoning or algebraic calculation, it is not sucient just to write
the answe
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
MATH 233
EXAM 2
Spring 2006
Student ID#
NAME:
Section Number:
Instructors Name:
In problems that require reasoning or algebraic calculation, it is not sucient just to write
the answers.
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
MATH 233
EXAM 1
Fall 2006
NAME:
Section Number:
Instructors Name:
In problems that require reasoning or algebraic calculation, it is not sucient just to write
the answers. You must expla
Practice problems from old exams for math 233
William H. Meeks III
Disclaimer: Your instructor covers far more materials that we can possibly t into a
four/ve questions exams. These practice tests are meant to give you an idea of the kind
and varieties of