M 408M - M408MF09_makeup_1_Sol - Fall 2009 - Rodin

# M 408M - M408MF09_makeup_1_Sol - Fall 2009 - Rodin - [1’...

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Unformatted text preview: [1’ tr. {3 Exam 1 Math 408M Name Fall 2009 TA Discussion Time: T TH You must show sufﬁcient work in order to receive full credit for a problem. Do your work on the paper provided. Write your name on this sheet and turn it in with your work. PleaSe write legibly and label the problems clearly. Circle your answers when appropriate. No calculators allowed. Discussing any part of this exam with a classmate who has not yet taken the exam is considered scholastic dishonesty. 1. (12 points) (a) Find all polar coordinates representing the point whose cartesian coordinates are (17,31) 2 (—5, —5\/3). (b) Find Cartesian coordinates representing the point whose polar coordi— nates are (736) = (— ,—%T). 2. (13 points) The curve C given by parametric equations a: = t2, y = t(t2 — 12) intersects itself at the point (12,0). Find the equations of all tangents to the curve at that point. 3. (13 points) Find all points of intersection of the curves C1 and C2, where Cl is given by parametric equations :17 : Vrt, y 2 v4 — t, for 0 g t S 4, and Cg is given by parametric equations 51' 2 es — 1, y = 265 — 27 for 3 Z O. 4. (a) (12 points) Sketch the graph 7' : 2sin49 for 0 S 6 g Label important points and angles clearly. (b) (12 points) Find the area of the region lying inside one loop of the curve 7" = 2 sin 40 and outside the curve 7' : 1. 5. (12 points) Set up (but do not evaluate) an integral representing the 2 2 a: circumference of an ellipse whose equation is given by 7 + %2- = . a . 5 6. (13 points) Graph the conic given by the polar equation 7‘ = Clearly label important points on the graph. 7. (13 points) The vector 17 has magnitude x/2 and makes an angle of if with the positive x axis. The vector 13 has magnitude 4 and makes an angle of 7r with the positive 3: axis. Find the magnitude and direction of the resultant vector 17 + 117. Bonus problem on back. 45m“? Moi» Etiquwn-f, ggqqg So wfossalu Pam (4mm {0 (-5,-“53 GM— CIO) ‘HYg+3le') M C—lUJ W3+91¢1T) Law h—I'S wmmhyb (53 (he) = (~2J—7ﬂ75) Xch,L 3 =HJJ=IL> = t 4% 42"(1370) t=iVTi =iaJ§ 0:33”: M/Jt _ Sta—12. o‘er/Jt at VJLJM {7: éH/E .. 3942' .. ~9— .. ’ 33.- 4r: ‘ r3 " 2E WU“ t3—SVE a 2 36-”. ‘ﬂ—aﬁ M —m " bsafﬂx—la) mot 3:—a\/§/x—12.) To zflkok HA. §>ohf\$ W .94 =7 05x52, (saw xz03 So C‘Baﬁuakurob WWCIA‘ﬁWZ/ JI9N3 miffed» zywi/I' ﬁu‘lM. . S .8 Ca. Xsc -1 2:7 9:14.] (Iv/Kumw 4W5 044.: Inmmh‘m 2 SM 3x: m ) psxs-z. HXZEQ-xz‘ 53334 sttyf 3:) x: /V3_ swab-:3] +14 fang/+1 MWcJTM '6 (3/6: 943.) 4(a) kcélsmw 05—95% yu k = rap 3 QW‘FQ IS PWML'C UJ+L flu/WA £2,772. .TLQ 3mm FzQS’mq’Q but“ M Wyv»; s} 930/95W9 M 937172.. . ' P‘ owl/l E! P094101 4"“ (799an M0! "mam Jn “74599'771 ' r (law WC!» 1+3 Maw 5m“ .L SE {—(44-8'9 : 3g 4%149 ~\ 009: 23 ‘f( “2 )4” I qu “‘ 5-“?1.¢ .. J. \ u] — 2,5 [—96008’949 =2[Q—éng—} 1I72"! 1919 UT : j \/(_q%9)2'+ (L009)L €19 0 2V 3L W 49 ...
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M 408M - M408MF09_makeup_1_Sol - Fall 2009 - Rodin - [1’...

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