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ReviewMath2224Fall2007_4

ReviewMath2224Fall2007_4 - Math 2224 Common Exam Fall 2003...

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Unformatted text preview: Math 2224 Common Exam Fall 2003 FORM A Instructions: Please enter your NAME, your ID NUMBER, the FORM DESIGNATION LETTER and your CRN NUMBER on the op-scan sheet. The index number should be written in the upper right—hand box labeled ”Course”. Darken the appropriate circles below the ID number and form designation letter. Use a No. 2 pencil; machine grading may ignore faintly marked circles. Mark your answers to the test questions in rows 1— 14 of the op-scan sheet. Your score on this part of the test will be the number of correct answers. You have one hour to complete this part of the final exam. ' (0)9) , J) bl? 1) <1 we ’0 *IC (0 ‘) f\. liberal/flu: 4(01‘})+’g7‘<01‘)0($ ) 7 J C3 101 e'i‘iaqfi MD, £3: 27"“[6 gxf‘ 7c “k; .. ‘D [1] The linearization of f(:r, y, z) = x2 + e” + yz3 at (0,1,1) is 9% ’ Us 1) 333+22—y+1 2) —2+x+y+32 3) —2—:z:+y+3z 4) 2—x—y—Bzz0 2 _ 2 _ _ L [2] The limit 11m u is X ”Y > G 3, (mm—40,0) 2332 + 1/2 .. - 1 3‘ «0 _) I 1) 1 2) E 3) —1 @Does not exist [3] The direction in which f (m,y) = 2mg — y2 + 3x2 has a maximum rate of change at (2, —-1) is ‘7]? (2'4): (Ix (3,4)) 1) 105+ 65' 2) —101— 65" 3) 101'— 65' 4) W371 . ' 3,»; (2,4)? . _ 2 _ 2 . 1 [4] The contour map f01 f (3:, y) — :1; 4y ceiisists of {.210 \1' MA 1 X >’ L‘ 2: l4» 1 1) Ellipses only 2) Circles, and a single point ‘1 V—’-¥° hkjpmblgj 3) Hyperbolas only 4) Hyperbolas, and a union of lines [5] Let f(:c, y) = g(u, v), Where u and v are functions of a: and y, Where u(1,l) = 2 v(1,1) = —3 1- 1x: 3“. ugfiv'vx u$(1,1) = 5 vz(1,1)= 1 V! \v 9112—3) = —2 9112—3): 6 {\ [(23 The partial derivative fx(1, 1) is 1) —4 2) 4 3) 12 4) —§ [6] A lamina occupies the planar region bounded below by the :r-axis and bounded above by the circle :32 + y2 = 4. Its density is p(cc, y) = 3:2 + yz. Its mass is 87T 6471‘ J ‘ 27r _ 7r _ 1 1) 2) 3 C394 4) 3 [ 1:“ ”t 2 055'; j 3 N j a rattle f]".fi,w’ L; o [7] The volume of the solid bounded by the surfaces y = 2:2, z = O, and 23/ + z = 2 is given by the integral @1:/;/02_2y dzdydx 2)/_11/0x2/02_2y dzdydm 3) 111/3: Afgy dzdydx 4) [11/0262 /02—2x2 dzdydag 7k If} _ 2 1 [8] The value of / / 7rsin(7ry2) dy rim is 0 30/2 1)—1 2)1 3)2 4)3 [9] Which integral represents the volume of the solid inside the sphere m2 + y2 + 22 = 4 and outside the cylinder :32 + y2 = 1 ? 27r 37r/4 2 2_ 21r 57r/6 2 2' 1) /0 fm /1/sin(¢) p sm(¢)dpd¢>d9 @A [W /1/sm(¢) p Sin(¢)dpd(/)d0 27r3 27r 37r/4 2 27r / 2 3 / 2 ' d d d6 4 / / 2 ' d ,6 )/0 -/7r/4 1/8050» P s1n(¢) P <5 )/0 ”/3 l/sin(<i>) p sm(¢)dp 45d [10] In the use of partial sums to estimate the sum of the series co 1 oo _1 71. 2-7 2 —2 and Z ( ) ,vvhich of the following is true? In J 2 B 71:1714 n=l \TL/ ‘1 H: 7.} 2566‘ . 001 3 1 1 oo _ln 3 _1n 1 “.3,/ ~/1)Z———Z—_—andz(.)—Z( ) g— x» z _ n2 _ n2 16 _ n _ n 4 ' f» ,l’ n—1 n—1 11—1 71—1 6”" ‘6 v ii~ii>laiidi(_1)n~i(_l)n<l 71:an F1722 16 77F; n “:1 n _ 4 1‘6, 3) i 1 :3: 1 > 1 and i (—1)” i(_l)n > 1 71:1”2 n=1 ”2 16 n=1 77’ 71:1 77/ 4 oo 1 3 1 1 oo (~1)n 3 (_1)n 1 4 —~— —— < — d — ~ )Tgrfi Eng—16am ”2:21 n T; n >4 [11] Which of the following series converges? °° 1 °° °° (—1)” °° n n+1 W 1 —— 2 —1 n 3 _——@ < — > )Efl/fi )g( ) )gn'cosmvr) >712; n+1 n+2 33v 111:" 3 n(n+2)-nzv:zn~i (Q ”~7— 2 \ (mom 2) a. n1! ,_ l dhr ”"fi‘ = H” , L (anYH’L) m 2. PM I “ ‘ ~V‘_ w. ‘v'v' L~~" "' K 3 0° " '2. e =l+X+L+L~"§—§ .2‘. 5‘. Mm, 9 e—Xr’l" a—&+¥_fa" [12] Which of the following is the Maclaurin series for f (cc) = 6“”“2? no 52‘, 3" n an 00 33271 00 ___1 71.23271 00 (_1)nm2n 00 $211 3 (:4) X. 1)Z—2 , 2>:—( 2). @Z—— 4> ——, 7 N n=0 ( n)‘ =0 ( n)‘ n=0 n 71:0 7?" (if—b ' [13] For the power series 2 2”(4:13 — 1)“, which of the following is the open 2.]L1V~l l 4] 71:0 interval of convergence? [L] x —l \ < ]5- 1><giz> sea mes) Ave-:5) 13‘2“? 1 00 TL TL [14] The series 2 ak has partial sums Sn = Z ah = <1 + a) . Which of the l\ Y1 n: 6 [i=1 [i=1 following is true? 00 1) The series 2 ak diverges because, for every n, 3” 2 1. k=1 00 2) The series Z ak converges to 1. k=1 ‘ 00 @The series 2 ak converges to e. k=l OO 4) There is not enough information to determine whether the series Z ak, Ic=1 converges or diverges. ...
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