Math 164: Multivariable Calculus
Midterm Exam 1
October 18, 2012
NAME (please print legibly):
Your University ID Number:
CIRCLE YOUR INSTRUCTOR:
Fili
Madhu
Mahmood
NO calculators, cell phones, iPods or other electronic devices are allowed during the
exam
MATH 164
Midterm 2 ANSWERS
November 21, 2011
1. (12 points) Consider the function f (x, y) = x2 y 3 + 3y + 1 for (x, y) R2 .
(a) Find the critical points of f .
(b) Find the local maxima, minima, and saddle points of f .
(c) Are any of these points global
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Math 164: Multidimensional Calculus
Midterm Exam 2 Solutions
April 3, 2008
Name (please print legibly):
University ID Number:
Please check the box of your instructor:
Thomas Tucker MWF 1000-1050
Andrew Ledoan MWF 0900-0950
Calculators, cell phones, iPods
Math 164: Multi-Dimensional Calculus
Midterm 1
October 21, 2008
NAME (please print legibly):
Your University ID Number:
Indicate your instructor with a check in the box:
Nicholas Rogers MWF 10:00 - 10:50 AM
Sema Salur
MWF 9:00 - 9:50 AM
The presence of c
Math 164: Multivariable Calculus
Midterm Exam 2 ANSWERS
December 3, 2012
1. (15 points)
Find the extremum points and the maximum and minimum values of the function f (x, y) = exy subject
to the constraint x2 xy + y 2 = 9.
Answer:
Let g(x, y) = x2 xy + y 2
MTH 164: Multivariable Calculus
1st Midterm Exam ANSWERS
November 1, 2010
Part A
Important Formulae?
dT | r (t) r (t) |
(t) = =
ds
| r (t) |3
(x) =
| f (x) |
[1 + (f (x)2 ]3/2
a = v T + v 2 N
aT =
aN =
r (t) r (t)
| r (t) |
| r (t) r (t) |
| r (t) |
MTH164s07
Sample Final
Exam Time: Mon 05/07, 4 - 7pm
Name:
Student No.:
Instructions:
Answer ALL questions from Section A
Answer ALL questions from Section B
You may use a handwritten sheet of notes. Calculators are NOT permitted.
Read all questions c
MATH 164
Final ANSWERS
December 21, 2011
Part A
1. (9 points) Find an equation for the plane passing through the points
(1, 0, 2)
(1, 2, 3)
(0, 2, 1)
Answer:
Call the points p, q, r respectively. We need to nd 2 vectors parallel to the plane. Subtacting,
Math 164: Homework #1, due on Wednesday, January 13
No late homework accepted.
Reading: Chapter 1 (sections 1.1-1.5)
[1] (Fitting a quadratic function to data) The following points in the plane
are assumed to lie on the graph of a quadratic function (t, b