, \_ "
1. (a) (10 pts) Consider the function f (x, y) = 3x2 xy + y3. Find the rate
of change at (1,2) in the direction of v=2i+2j. r:
u ,
(b) (10 pts) In what direction (unit vector) does f increase at (1,2) at the
maximum rate?
a- du/(x(§)=VF'M M= \V 3
1) Find the equation of
n x x 1
2) Find the volume of the pa.
where P = (.2,0,:;1),Q =i(4;,
\F: 5U (1)136.) m WA Pam
silofwlr 13%
mt: («n1 ZR
(11 +05) MATH 2210-02
QUIZ 4
Wing-irO q
Hg+Zx~2=O
4(22A +ZxIZ9-{é
6-8: + 2x~2=0
:QL: Ca.-:bA
mm) = 2010 + 2m;
MATH 301/601, Final Exam, May 5, 2007
1. You are dealt a poker hand. Below is an expression for the probability to
get three of a kind but one factor X is missing. What is X?
13-(§)-X-4-4
(as?)
*******************************************************
Math-122 Final Exam
29 April 2011
NAME:
PROFESSOR:
INSTRUCTIONS: This exam has two parts. Part 1 consists of short answer questions for
which you write only answers. Part 2 consists of work-out problems. Write neatly and show
all your work in the space pr
Math 221 Final
December 11, 2007
Name:
Instructor:
Section:
INSTRUCTIONS READ THIS NOW
This test has 14 problems on 15 pages (including this one) worth a
total of 250 points.
Write your name, your instructors name, and your section number
right now.
Sh
Math 221 Final Exam, ?
Total points: 200
1. (5 points) Given the nonzero vectors a, b, c, if a b = a c must b = c?
Explain.
1
2. (10 points) If f (x, y, z ) = x2 y 3 z 4 , nd the equation of the tangent plane
to the surface f (x, y, z ) = 648 at the point
Math 221- Several Variable Calculus [Vitter] Exam Dec. 8, 2009
Print your name at the top of the rst page. Work each problem in
the space below its statement. JUSTIFY all your answers and show all
your work NEATLY. Put a box around each nal answer.
1.Find