MATH 2063 Multivariable Calculus
Section 3, Spring 2013
Instructor: Prof. A. Lorent
Ofce: 4109 French Hall
Ofce hours: to be announced.
Email: lorentaw@uc.edu.
Text: Calculus: early transcendentals (7th Edition, with Enhanced Web Assign), by J. Stewart. B
Math 2063 Review Problems for Test 1
1. What shape is described by the equation x2 2x + z 2 + 4z = 4?
2. Write an equation that describes points P (x, y, z) that are the same distance from Q(3, 0, 1)
as they are from R(2, 4, 0).
Multiply everything out an
Math 2063 Review Problems for Test 1
1. The equation (x 1)2 + (z + 2)2 = 9 is a cylinder with radius 3 and center axis given by
the line x = 1, z 2. It is parallel to the y-axis.
p
p
and |P R| = (x + 2)2 + (y 4)2 + z 2 .
2. The distances are |P Q| p
= (x
Math 2063 Review Problems for Test 2
x2 y 3
does not exist. Evalute the limit
(x,y)(2,1) x + y 3
a) as (x, y) approaches (2, 1) from the x-direction.
b) as (x, y) approaches (2, 1) from the y-direction.
c) as (x, y) approaches (2, 1) from the direction of
Math 2063 Review Problems for Test 2
2
4
= lim x+2 = 4.
1a. As (x, y) approaches (2,1) from the x-direction, y = 1 and x varies. lim xx2
x2
x2
1b. As (x, y) approaches (2,1) from the y-direction, x = 2 and y varies.
lim 1y
y1 y1
= 1.
1c. As (x, y) approac
Math 2063 Review Problems for Test 3
Note: Many of these problems ask you to compute integrals, some of which may be complicated.
It will be most important on the test that you are able to set up the integrals correctly.
Only a few test questions will ask