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Unformatted text preview: MA 261 Name Student ID EXAM 1 Fall 2007 Recitation Instructor Recitation Time Directions 1. Write your name, student ID number, recitation instructor’s name and recitation time
in the spaces provided above. . Write your name, your student ID number and division and section number of your recitation section on your answer sheet, and ﬁll in the corresponding circles. . Mark the letter of your answer for each question on the answer sheet as well as in the test papers. . The exam has 12 problems. Problem 1~8 are worth 8 points and problem 9—12 are worth 9 points each. . N 0 books, notes or calculators may be used in this exam. CL QQC/g Agaic 1. The projection of the vector V = i — 3j + 4k onto the vector b = i +j
is A. projbvz —i—j 1
B. ro' v=—i+'
p Jb ﬁ( J)
. 1. .
C. pIOJbV=§(1+_})
D ro' v——L(i—')
' p .]b W J . 1 .
E. pI‘OJbV: §(1—_]) 2. The area of the triangle with vertices at (a, 0, 0), (0, 2a, 0) and (0, 0, 3a)
is 3&2
A A:—
2
B. A=5a2
7a2
C A";
D A=6a3
3
E Azgi 2 3. The graph of the surface 3:2 — yZ + £2
9 = —1 looks most like : B 4. A line L contains the point (1, 2, —1) and is perpendicular to the plane
33: + y — 52 = 1. What point on L intersects the plane y = 0? A. (9, 0, —5)
B. (—9, O, 5)
C. (5, 0, —9)
D. (~5, 0,9)
E. There is no point of intersection 5. Find spherical coordinates (,0, (9, <75) for the point P whose rectangular coordinates are ( 1 ﬂ, 1
ﬂ: 21> PU .0
“N 00
PM: 001:1 Mile cola A>l>1
CM: ms Na Na DJ=I
V \_/ \_/ V \_/ O
/‘\/—\/\A H
/—\
UN 6. The unit tangent vector to the curve r(t) 2 (cost, sin 3t, €t> at the point (1,0,1) is: 7. Find the length of the curve r(t) epcwe 3 1
07—,—
< 10 10>
1 1 07—)—
< 2 2>
~1—1
13,—,—
< \/§\/§>
—1 1
Oa—aoaﬁ
< ﬂ ﬁ>
— 3 1
<W’U’W
2
4
6
8 10 8 . Evaluate
lim x2e‘y (mm—42,0)
A. —4
B. 4
C. 0
D. 6‘4
E. does not exist 9. Find the domain of {I}
f($,y)=1n(y+2>
A. y7é—2, x>0 B. y>—2,x>00ry<—2,x<0
C. y>—2,:E>0
D. y>0,a:>0 E. y>0, $>00ry<—2, x<0 10. Compute the tangent plane of the surface 2 = 2533/2 — E at (2, 1, 2)
y A. z=x—5y+5
B. 2:56—63/ C. z=x+5y—5
D. z=2x+y—3 E. z=m+10y~10 11. Hz 2 :L'2+y4 and x = —211 and y = u—v, compute % at (u,v) = (2,1).
A. —4
B. —12
C. O
D. 4
E. 12 12. Find the rate of change of the function f($, y) = 2x + 3y at the point
(1, 2) in the direction of the vector v = 3i + j. e .U .o .w .>
gt “9 Elm 8'0 51w ...
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This note was uploaded on 04/07/2008 for the course MA 261 taught by Professor Stefanov during the Spring '08 term at Purdue.
 Spring '08
 Stefanov
 Calculus

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