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Unformatted text preview: 2008 Fall Math 230 MIDTERM
Tuesday, Oct. 23, 2008 Instructions:
a print your last and your ﬁrst name on the ﬁrst and on the last page
0 This exam has 7 problems.
Please make sure that all pages are included.
0 Show all your work on these sheets. Feel free to use the opposite side.
0 Make sure that your ﬁnal answer is clearly indicated
0 No calculators, books, notes, etc are allowed. LAST NAME, FIRST NAME: 20 Problem 1 (16 points)
Given three points P : (0,0,3), Q 2 (1, 0,0), and R = (0,4, *3). (a) Write the equation of the plane containing the points P, Q and R, and sketch this
plane, SUM $30 z~<4/o/3> I 1373 =‘<o/4/—{7 Ms) 9?“ 7‘) — '\ 3 ~ '6
w. \ale?“ ,\ O _3 “mu 6/ 4>//<,2,22
o 4 ~63 +Bj+2(2~—>>'):o. ,9 —2 y W (b) Find the area. of the triangle APQR. 101 3:3 Ifﬁxﬁﬂ ‘ '2. 1 ‘L. 1
‘Evffé + 7+ 42 . ,__.~ Problem 2 (10 points)
Find the distance between the parallel planes 2x + 2y — z = 1 and —2:2: — 2y + z = 0. Problem 3 (15 points)
Determine whether or not the two lines £1 : :1: = 1 + 275,3; : 3t,z : 2 u t and £2 : 3: : —1 + 3,1; 2 3+ 25, z 2 3 are parallel, skew or intersect. If they intersect, find the intersection
point of the two lines. 2:1“va {3: z < 1/ 3/ "l > 01:“ ‘>— 0> / _,
rxl /\ Ut,0iw& wwwydLK ":9 Qﬁ / Q1 9xva wmw 6) V__
TWA _ Mg :3 9:0 3%: 3+2g —J© gtn
2“:9i : 7) 4—1:) "v 2 ~51 ~15 We it,th
":5 191,971 909 heme; £«IELRHL SLEKQ‘ W Problem 4 (20 points) Consider the surface y? 2 2
+ _ _ 42 0
LE 4 pOthS) the traces Of the given surface 011 each coordinate planes and sketch a graph of the surface. Make sure to clearly label the coordinate axes. (ii) (4 points) Identify the surface (Le. give the name of the surface). Cma
/ Problem 5 (10 points)
Convert the equation of a curve given by r : 4sin6 + 20086 in the polar coordinates into
an equation in the Cartesian coordinates. Sketch this curve. ‘7. . r :, 4 r3?“ 9+ area“) 8 KWRjmz4‘j 1‘ 2 X 4:) (x4): 92$”: 5 ’A O > Problem 6 (15 points) Let the curve I be given by 332200536? W
(0593 k)
y=251n39 2 (1) Where the tangent linesbo the curve are horizontal? Se.me igﬁz :_ @338
)0 A ~ w
’15— _—_O :3 E 6 L
(‘dﬂ—J—‘hﬁ (2) Find the equation of the tangent line at (3:, y) 2 (x/E, 1) (hint: cos 5. = g 2 (53:):__ %?G\ ____ 3
Z O YtnBS ﬂ
9%
—> Dug— :——E(X'—S W 'T" ‘V=*3 ;q_
ﬂ—L W 92—— ./ gag,
(3) Find the arc length of i. F
:o: 62x] 60 :1
e 4% L we:
2'” Q (Soﬁe) 9 )ngg‘ Problem 7 (14 points)
A body moves in space so that at time t the acceleration of the body is given by the vector
Emit) = (cos t)i + (sint)j i It. At t = 0 the body is at the origin and has velocity 43'. 1. Find the velocity and Speed of the body at if = Siblw'l‘ww: \(vumn : ﬁﬁ) : <Cﬂtl, Slml, *‘l> : (03/ o ,4 “A.
\I(¢3) 2 <0/ 4/ :12)
A ‘9: it \?<Ié>\: Echsmm ~= <§Cl S—Cﬁ‘l Bib LAST NAME, FIRST NAME: ...
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This note was uploaded on 11/23/2008 for the course CHEM 2101 taught by Professor Trzupek during the Fall '08 term at Northwestern.
 Fall '08
 Trzupek
 Organic chemistry

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