18.02 Multivariable Calculus
Fall 2007
18.02 Practice Exam 1 A
z
Problem 1. (15 points)
A unit cube lies in the rst octant, with a vertex at the origin (see gure).
O
a) Express the vectors OQ (a diagonal of the cube) and OR
, ,
(joining O to the cent
MA 113 - Calculus I Spring 2002
THIRD MIDTERM 04/09/2002 Name: - Sec': ~
002
TR 8100-9115, CB 349
m TR 3130-445, CB 345
008
m
011 M- 310116
012
Answer all of the following questions. Use the backs of the question papers for scratch paper. No boo
1. (a) (5 pts) If f(x) = l x2 and g(x) = nd a formula for (gof) (x).
Give the domain of (g of) (x).
(gafxx) = 3090) = ./ 1-x"
Jamal/(u: w. xs s/t 4-x 20
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donuuh : all ,KIS 5 [453x51 l
(b) (5 pts) Which of the following functions are even, odd, neither?
MAC 2311 Review for Exam 2, Summer 2015
This is an exam review provided by the Teaching Centers Math Study Center, located in S.E. Broward basement.
The Teaching Center provides walk-in tutoring as well as individual, weekly appointment tutoring services
*- MA 113 Calculus I Fall 2003 Name. Sec .
FIRST MIDTERM 09/23/2003 ' - "
SEC. INSTRUCTORS T.A.S LECTURES RECITATIONS
01 TRszoo-9zls,cmos
TR9230-10=4s,c1>103
02 TR9=3o-lo:4s,cmv
memo-9:15, BB 206
TR use-1:45, SRB 303
m Two-4:45, or 222
Answer all of the
MAC 2311 Review for Exam 1, Summer 2015
This is an exam review provided by the Teaching Centers Math Study Center, located in S.E. Broward basement.
The Teaching Center provides walk-in tutoring as well as individual, weekly appointment tutoring services
18.02 Multivariable Calculus
Fall 2007
18.02 Practice Exam 4 8
Problem 1. (10 poir~ts)
+
Let C 1)e the portion of the cylinder z2 y2 2 1 lying in the f i ~ octant (:L 2 0, y 2 0, z 2 0)
t
which gives the
and 1)elow t,he plane z = 1. Set 1111a triple integ
18.02 Multivariable Calculus
Fall 2007
18.02 Practice Exam 3 B
Problem 1. a) Draw a picture of the region of integration of
0
1 2x
dydx.
x
b) Exchange the order of integration to express the integral in part (a) in terms of integration
in the order dxdy.
MAC 2311 Review for Exam 3, Summer 2015
This is an exam review provided by the Teaching Centers Math Study Center, located in S.E.
Broward basement. The Teaching Center provides walk-in tutoring as well as individual, weekly
appointment tutoring services
18.02 Multivariable Calculus
Fall 2007
18.02 Practice Exam 2 A
Problem 1. (10 points: 5, 5)
Let f (x, y) = xy x4 .
a) Find the gradient of f at P : (1, 1).
b) Give an approximate formula telling how small changes x and y produce a small change
w in the va
18.02 Multivariable Calculus
Fall 2007
18.02 Practice Exam 1B
Problem 1.
Let P , Q and R be the points at 1 on the x-axis, 2 on the y-axis and 3 on the z-axis, respectively.
a) (6) Express QP and QR in terms of j and k.
i,
b) (9) Find the cosine of the a
MA 113 - Calculus I Spring 2002 Name. Sec -
FmAL EXAM 04/29/2002 '_ "
S
INSTRUCTORS LECTURES RECITATION
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007
ow
Answer all of the following questions. Use the backs of the question papers for scratch paper. No books
or notes may be used. You may use a ca