MATH118MS06S

MATH118MS06S - Faculty of Mathematics University of...

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Unformatted text preview: Faculty of Mathematics University of Waterloo Math 118 Midterm — Spring 2006 Time: 2 hours Date: June 5, 2006. Last Name: _______________ First Name: ID. Number: ________ Signature: Instructors: [:1 /Chemical Eng. D. Wolczuk El/ Enviro/ Geo Eng. C. Hoppen El Mechanical Eng. P. Pralat El Mechatronics Eng. R. Oyono Your answers must be stated in a clear and logical form in order to receive full marks. Instructions: 1. Complete the information section Question Mark Value above, indicating your instructors A name by a checkmark in the appro- priate box. 2. Place your initials at the top corner of each page in the space provided. 3. NO CALCULATORS permitted. 4. Tear off the back last page of the test to use for rough work. 5 Math 118 — Midterm Page 2 of 8 Initials: 1. Evaluate the following indefinite integrals TQM/a 5UESTE‘EKVQQM . 4 a “L d ,3 [ ] ) f W 517 (1:1 fir:’?fi‘g 9 [ghalech \ b1” dist: +0n35€09 X X Wfifi \ Subgwgn 3 “TVS 45 Tag SUbacomP‘e Siam/e 953% "anrh A'W‘S 5gb .hghs Math 118 — Midterm Page 3 of 8 5' powd flafihitials: ‘7? ‘ [4] 0) f 2%15 dm Uée Sub by (anWWEIBAg‘fle SCLUO “3.: j“ QQer‘ve/ .30LKAOXQ Q5: QQHQM\‘mj%\’br “w '2. ,‘ yl—V Cy +5 @Qf’arfimwv‘fl 4r\Y\ {V QLXWWWK QYN 26v h=O B: ‘fil M6 K: I t \ muld’vwmmflt :7 W”) +‘ 0* bogs k I QNL’QOYW“ «£60 Q (ha, 2 Tam/1 5:4 1551 17pm om . ,/ A ‘ . a ><:(s"+omfr’ * b, Double meow“ (M S otih 9 * v' \ KsedHC/m 09 @Omg *’ 3 gflmg _ W d8 5* 0(3’9 *6 r :fiWseflGdQ/‘jp’i/ gngQ +3 r f ‘migfidg * jjga/ +Om8+5 % x \ I (Lsz d8 5 " ( jfiiifi “‘8’ * \n\ +Om" d&%g%o\9 4/ \h :EVNWOHQ *Lfigjr \h \sm :5 \‘(\\’§OI\EV\ Jf\‘(‘\\$\ 1’ :@\n]\() Jrfly ’H “727%— A— ”Q) 2: -—---" 3 \7- M it: : i Math 118 - Midterln 7* 3‘ Page 4 of 8 Initials: 2. Evaluate the following definite integrals U = x +3 3 2x ‘ l4] 3) 0 «mdm clu=d><- mil—“Cghéxghj Math 118 - Midterm Page 5 of 8 Initials: b 3. Consider the integral f: cos dac o .1 , 5 [3] a) Estimate the Vfrlue of the integral using Trapezoidal Rule with n = 6. figzbflfimwae+§flnflrt*el¢*l%fiigl <:; : L:l YE _ym i2 K .,_.——d- ’— :WBN 1’“; - w fife—g New“ * aé"*fi\+_(—\+%l*(-l*% +(-I+%‘) >< _ \ y , 'ZT(—lr%l AIZ-Lml—Qzfi'ig ’“lél_‘“l / 4 m hie“7铧 [2] b) Use the formula Error 3 gig—35):, where M is the maximum value of lf”(av)| on a S as g b, to find an upper bound of the error for your A b estimate in part a). N1 we (1g) 3 M3 =/’”sml'i:>§lfll Err“ ‘4‘“ U2”). ~ “9’ / \DlQZ ‘ Nmflwflmw i 9* g1 9m) \QQQ li“”fl_ 4 a? ” “Zia” , A, " r 2. C¥ \VlQX- > 'll /L‘ /_ 3 - ’ 4e ":50 (g I OR ‘L'XL‘7/V ,Tej ( Q03<Ea>+ A§((‘J~l.,zr)+,(( to) +44“; Ailrfl :LCO ZEEE + Aer +Q+\~> 3 3 "".__.‘ >4 ’— BKLLVB @434; m ’2 \ "'1; -x— 53:25) ’19 V _. ’2 Math 118 — Midterm Page 6 of 8 Initials: 4. Consider the curve in polar coordinates 7“ = 3 + 381n6 ’) [3] a) Draw the curve on the axis. Show all steps used to arrive at your graph. 1‘ [3] b) Find the equation of the curve in Cartesian coordinates. ,, a; 3* gnggi _/ g Y2 (@038 8 ‘2 k\: (S‘\\9 “‘/’M / A 7 l X” i D M “ $33: :: A \I'i Math 118 — Midterm Page 7 of 8 Initials: 5. Short Answer Problems 1 [1] a) What is fsecrr dx? \fllSQCX 4)va xlw <— 2 dX a 3;” - O, [1] 0) Write the formula for length of a parametric curve (30,31) :2 (a:(t),y(t)), a < t < b ‘m (/7 94 /""Y l” \\ L b / 1' 7— m - ! 2W~"":--~——-~~-~~, Qj Wm) M “N ” J1 \f‘xMHy/e)?“ ta 1 d What is the formula for computing —dy for a curve 'r = 0 that is in dz polar coordinates? ...
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MATH118MS06S - Faculty of Mathematics University of...

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