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)
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 (
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
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 )
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) re
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
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
MATH 233
EXAM 1
Fall 2010
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In this exam there are seven pages, including this one,
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
MATH 233
FINAL EXAM
NAME:
Spring 2006
Student ID#
Section Number:
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In problems that require reasoning or algebraic
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 cal
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 i
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