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Unformatted text preview: EXAM 1 MATH 26100 FALL 2011 Name Student ID Recitation Instructor Recitation Section and Time INSTRUCTIONS:
1. This exam contains 11 problems each worth 9 points (one point free).
2. Please supply a_ll information requested above on the scantron.
3. Work only in the space provided, or on the backside of the pages. You must Show your work.
4 . Mark your answers clearly on the scantron. Also circle your choice for each problem
in this booklet. 5. No books, notes, or calculators, please. Mark TEST 01 on your scantron! WY DE E C /%/3E/4 0/4; i
I
i
g
3
g
; L 1. Let C be the curve given by ﬁt) = (Ah/i, t, 5 — 252) for t > 0. At what point does the
tangent line to C at (4, 1, 4) intersect the my plane? 2. The arclen’gth of the curve FOE) : 2t§+ £254 (111W? for 2 g t g 4 is:
17
I
B. 4+In2 C. 16+ln2
15
T
E. 12+1n2 A. D. 3. A particle moves in space With acceleration EL’(t) : at]? and initial velocity and position
given by 17(0) 3 5, HO) :2 3+ k. Where is the particle at time t = 2? A. (1,1,62)
B. (0,1,8)
C. (0,1,6—1)
D. (1,1,e2—2)
E. (0,1,62—2) 4. Suppose that z is deﬁned implicitly as a function of a: and y by the equation eyz + Sin(7ryz) — myz = 0. What is the value of g; at (e,1, 1)?
A. J
8
B. l
e
c. #1
71'
D. 3
7r
E. 1
e —+71‘ 5. The surface area of a rectangular box is given by the function
5(50, y, z) = 22:31 + Zyz + 2xz Where 13,31, 2 are its sides. These are measured as so : 10 cm, y = 20 cm, x 30 cm
; with possible errors in measurements as much as 0.1 cm. Use differentials to estimate
i the maximum error in the calculated surface area. 12 cm2
24 cm2 A.
B.
C. 36 cm2
D.
E. 48 cm2 i
60 cm2 ‘ l E
r
i
l
l
l
l
l 6. Given if z (1, —1,2) and 5: (2,1,0), ﬁnd 75 such that the vector ('2’: (5,73 — 1,2) is
perpendicular to (i X b. l
A. 75:1
B. H l
0. 732—1 1
D. t=——2
E. 15:0 7. The intersection of the hyperbolic paraboloid 3:2 — yz — z — 1 = O with the yz—plane
consists of a hyperbola and a parabola a hyperbole, an ellipse two lines $50573?” a parabola 8. Let ﬁx, y) = V902 + y. The equation for the tangent plane to z = f(x, y) at (2,1) is 9. The critical points of f (x, y) = 351:3 + 3y3 + 1133y3 are: A. 2x/5z—4m—yzl B. 2x/gz—4x—y = 10 ‘ C. 2z—2m—y=l
D. 22—2m—y=10
E. 2\/gz—2a:—y=9 A. (0,0),(1,—1) B. (0,0) C. (1,1) D. (0, 0),(—31/3, —31/3)
E. (—31/3,—31/3),(1,1) 10. The directional derivative of the function f(a:, y) = ﬁlmy + emy at the point (0,1) and
in the direction of 17 = (3, —4) is: (5, 0)
<3) ”4)
—15 magma?» 11. If then 5:): is: (3t Z: 152 + l '1}, “(3,73 = 75+ 52, ”(3)” =1n(t) —(1+%~> ' (t+32)2+1nt
—<2<t + 32) + 113?)
(t+32)2+lnt
~(2(t+ 32) + %)
' ((t+32)2+lnt)2
—(u+1)
' (um—v)?
—(2u+1) ”LagH) ...
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 Fall '08
 Stefanov
 Calculus

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