W10MTH240Test3(Soln)

W10MTH240Test3(Soln) - Winter 2010 MTH 240 th 3 Last...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Winter 2010 MTH 240 th 3 Last Name:(Print) Student Number: Last Name ( Print ): Ryerson University Department of Mathematics Test 3 MTH 240 Calculus II . Signature: Date: April 24, 2010, 9:00 am Duration: 1hr. 30 min. Instructions: in . Have your student card available on your desk. . This is a closed-book test. Notes, calculators and other aids are not permitted. Verify that your test has pages 1~7. Do not separate the pages of this test booklet. The point value of each question is indicated by the question number. . Include all significant steps in your solutions to the questions, presented in the correct order. Unjustified answers will be given little or no credit. Cross out or erase all rough work not relevant to your solution. Present your solutions neatly and Iegibly in the space provided. Messy or illegible solutions will receive no credit. If you need more space, use the back of the previous page. Indicate this fact on the original page. . First Name (Print): Professor (circle one) Dr Homayouni Dr Tasié Section : For Instructor’s use only. - - Dr Olivares Winter 2010 MTH 240 th 3 Last; Name (Print): 2 1. [8 marks] Find the radius of convergence and interval of convergence of the series °° 2"(r—3)" h __-5)n Pa} (1 = 2 (x than n NI n+3 ) 1 f"_"' r'" I‘m and-0‘ : t‘m 2n+1(x‘5)nf _ “*3 2'th )2(X—'5) m 3. he, 6-0 dn has... m7; 2" (ac-5)" n-p—o in“! =2lx-‘31 ltm .32 a 2 ‘ x-‘Z‘H ’ 91"!“ (7:11 (Go, 417?“: sc‘l‘l‘ts converggs ka le-‘B‘ < 1 <%* ‘ Ix~bl< - «=9 -~'i<x-5<—‘£ <=> .30“: M 9» 2. 49L“, rad‘tws o-F Convergence. 435 R ai , ~ (4)" 0- ~ . . ‘l n ’1» Len 3c: .3- vae sc-r‘tcs bananas Z ‘55 = 5—3- nsl m h=l {n+3 .. '7 .14“ - I x- a sew-res becomes Z“ 2” ‘2“..‘_ 2": i ngl W hat “1+3 \ ~ '— n The, series ELL) converges Bu 73w. A.$.T rial Yh‘rb “W5 (inverqu wars €30) 7th {n+ervaj 03C go-nvekama is C 3’1) Winter 2010 MTH 240 Tast 3 Last Name (Print): 3 2. [ 8 marks] Find the Maclaurin series of f (1:) z arctan and its radius of convergence and interval of convergence. w ‘ (W ’_ W (at) €‘+ ( [+2x )2‘ \«2X ‘U_2%)Z+U+zx)2. W 1—2:: zyrfl-ug/ ‘ 4 _ J4” = 2 z 1%4xhuflxmrz 2+6“ 10+“? “'31 ~ ‘ 7' I - 2- 21: @433)" ~Fur l-4x‘l=4lxlz<l @kaé ‘~'(-‘43cz) 31:0 09 :: 2 Z x211 h-D NOw accx)=/(2-Zj.7€4flxm)dx =2. immfléx-2-§64)"Jx”'dac :2. ~—4"-E£i3“ _l_ B; QC) in” +c ,5,» lacl<z (3.14 R 2 .— Smce, £10) 1: achcan 33.9 : arc’ron1: if we, cad‘ {lth'ZOi-C % C = 2?". )1n+l do 21111-1 0" L_”'b 0°: Gd)?" '° m . l . 4 x. a __ z _ ____, . (-0 50’) I; 3C 4 ‘2 2 "Zr—’06. ) Zh+1 2 “Zn; 2 (2(1445 ré 2"“ 3am" wkcck converges bat vela— A.6.T- REM/(M: 1:; ¢ domam °‘ am I 1 [12:1 w 96 17“ ~—- 5 a: < - and, 5°) §cx):2-Z,DE4)'2M1+4 , ,1 z z ic—m- sz-acym + Z 3 “=0 2n+1 ‘f Winter 2010 MTH 240 Test 3 Last Name (Print): 3. [ (5+3) marks] Given the function f(1t) = \3/1 ~ 1: (3.) Find the Taylor polynomial T2(r) about the origin of the function f (1:). ~l-Lo)=i ) 2 2. -- l lynx): .2'; (lex)‘3(—1) = «gm—x) 3 => Hob—~13 -5 _§ , 1“th gum) 3-(-1)=-%c1—x) 1 => Wow—7% 50' , TICxla Fto)+‘c% x + $‘é?)x1 :: 1~1 _,_1_ 2. . bx 93° (b) Use the Taylor polynomial from (a) to approximate V3 0.97 Hz) 25 Ease) M=m3=3 [00 l l —< .. ._.—. _. ~..—— —- _. l .- lOO lOOOO l—l =f(,~%)x£l1>=l—l.i~ 9 O 10000-400 -l 98 lOOOO Winter 2010 MTH 240 Tat 3 Last Name (Print): 4. [ (5+5) marks] (a) If u = 2341; + y2z3, where 2 t 2 x=rse‘, y=r3 e’, z=rssint find the value ofg"; whenr=2, 3:1, £20. U.?x+’cfl.&.2‘4+fl.23 x 3 7376 72 75 _ 2 - x. -Tet+ (:Jc"+25z?’)21‘.5et 4- 33222” an” L2” V Auk-eh +=2l 5:4 t=° what/f. 31:2, L3:52, 2:0 I 50') 1%(2,1,o)=cq-2+1C-4 +O-O:192 (b) If 2 = f(a: — y) where f is a differentiable function, Show that 25 + gfi = 0. 3'3- =f’cx-3) Jun-g)- (—1) 2; ’o‘x ’73 ‘90 15+2—Z':O 1‘ 3x TU Winter 2010 MTH 240 Test 3 Last Name (Print): 5. l (4 + 4) marks} Let u = u(1:, y) has continuous second-order partial derivatives and let .rzr—s and y==r+2s. 3 33—2!” W15. 29a [914 '1“ 7-1" 77c 75 7x, 5;?“5'55 ’}‘7‘_2 95 I ——_—- )M:“—- 7x 55 x 9 Elli 23-; 7‘3 5 ’m’3 122,2. 2.! =2.(Z!.2r 9.31%; 71 ’73 wt 71‘ 73¢ 73 m ’ax v5 :- 1 2:?Jiai2u. 2r } é’éLlaLZL—l).2§ gr‘braw "5:5 5%2’71’37873 =(2 7‘“ 41W L+(Z&-i&4).i b 271 57F35 5 297531" 3 J?- 3 . 9:23.! “LL” + 12:21— 421k 9 71“ 9W7: 973W 9 7.51— — 2: 37'“ .L 91% I (flu. 311$ .Z‘LJ: ‘ 9W1+9wn‘7§ 731 Sm“ was arr” Winter 2010 MTH 240 Test 3 Last Name (Print): 7 6. [ 8 marks] Find the absolute maximum and minimum values of f (:c. y) = 4W2 ~ x2312 - £113 on the closed triangular region in the ry~plane with vertices (0.0), (0,6), (6,0). We first Solve mside W madam. g Hebe. 231. 431.21.51.33 ) 33538134123413: £30 :1!» 463(19-432—3) so 4 fine OR 4—2135. PM: 45-0 Cm‘b Cn‘h'de. ’2‘ ’4‘22’. %:Q (a) 1J(8-2x~)3)m (0,0) L. up) ‘1’ 1-0 a! 4‘2“- =0 on 8-21-12+6z so 130 {m'e- Chfi‘dg ) wkm 1:2 moist- 3:0 and (2,0) Cfin’i— fins—{dz ms Hm. one, crib-tau, rum-t L‘de is (1,2) aux. fa On, L(, 530 ffix,o)so :21-4. 04' L; , fizz-3+4 and. JCC‘5+£,5)=-231("3)--|231+733 f’:-24za+4%1=6701_4) ++o------++» Crih‘caL paid-s arc I3=o ’fia‘g /.\»‘:/‘ fa’o) ‘0 “"‘L fC2/4)=-64 04‘, L3 , tau-o I fco,J).«o' f I 6r) em Hm. winch. M35011 3" «Mm mameJe Max «1: (1,2) Mit’x {CHM-4 anal Ha. abaoeuzt. «ha-71. at: (1,4) 4.4..in funk-64, ...
View Full Document

Page1 / 7

W10MTH240Test3(Soln) - Winter 2010 MTH 240 th 3 Last...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online