Midterm3v1Solution - Midterm 3 March 22, 2011 (10 pts...

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Unformatted text preview: Midterm 3 March 22, 2011 (10 pts /2l]r12 dx = @ z .2 (1) > 1 We“: ’3; [EM/9,1 WWJ 'ma/“fémai‘xk :1: my .2 M, :5. mac 2 x&2(%g/—z[z.aé/-;z-§ gig I ‘z I {at aygpméfiujf (z 612(’)—Z-2 Zq/fz. — .. (1.54162)- 2,1,&4(E’_)+1): 6’- £4112 +Z&L‘Z 24-141 -&IZZ_ ,' ' vi grizfléfr a” _— h'H (a) (15 pts) [:0 2$€_m d1: 2 (flag 7Pear 7:— [— .5/275_ {_ . —;a var] SWW - - , am [12:01; 4— 2e : _t:oo Sixeflcg‘t—wfl 0 0/ —7e0 at t - ‘2‘ St 0502 : Zorn (—2.29, ~28 I: &m (‘Zze’zz'hz Ff t-aaa t O '2’ z e’ ——» _ 3P: Q—fim 02—15%; gt ftp—Z 4:. Wm: fSChadt cm‘w = [(l-w12)<fi%b‘)o€x : 2 .72 ° 3‘5}; TVZ o 1’ "Va 7'72, at; “my: new =5! 54— 1+“; 9‘ mason-Ema»): o 7 7- o o : 2. sin‘we 2) 2 E 1W5 o q o ,6 Fuu {of WWW <2-5)(7c +‘{ , 43 CM” 4 1,.-L : “4+3 0773 792%” (2221‘9/ +E(X-5 Xi! (xgg)(xI—_}y) AZ 2- 43’ ,_ 1.1/15 Cx$+DX—9C7‘ 99+FX 75—— 1 [2r 4% +Lffla: 90,943- ”M/ 5- 33f}: 7? 36": /5 M L -5; _’/—arc7fin 31—4—6: :E&/’H/ Iaé/X’L3/7LW5 5/73 X . (5) Use direct comparison test or limit comparison test to investi— gate convergence of the following integrals. (a) (10 pts) iii—9‘? p/ gawk,» 7/uua745h . ~ , 344 ’1 We" EMS”: 9:, Jaw F {+55 — 5m mflv fig”; m? “we “'6 . -uflé My ' I we 53% “@713 as /” i . "’ D x M I fizz-W150” 7.4”! I, Mil/(W é %/W5Mf (b) (10 pts) 000%??? 00 _; ' 0<I/<~/x/=eaozfl’ ‘Mfmm i/K-féx e f -E I ‘L - ’ 4" 3 Va ‘ g ’ (,éé x .2, Séézaéx / 6"” “It/e — raga ’— -e—>W 0 (6) (10 p2: Find £1310 WNW é! n/ /¢(n{/)‘ n4- , . fl; L ,& Zn “713—? fiWMZA “1’; I‘m?” / “,7” "I/ 1" r2. ,— L tr?” (ml) (“57 w WW» 5;» (%) = e / Ill—>90 M (7) (10 pts) Does the integral / ‘1‘6—1'2‘ dzc converge or diverge? o z 00 2 Explain your answer. _ ~?< 39(M1'm: of xe‘f/agw “My/A1419“ We «(/0 1 Op ’0: D #10 fl ~roz< :—_ OS,xe—)c +§xéxo&c:—-5K€ool><+sxe : o 9-5 (00 D x10 _t gojz P:_€W {xéfix+zmygfieab<s t—a—V‘t x10 ‘69‘ 0‘ —L.é_ .le: [-1— 5M ‘26” ‘ 2+5 :‘fgfl’wt 1-1 1—99.” I_:z—L =l+ihi ' n ’l+J—e:'t)+g‘m (—iQ +2. 22,, (8) (10 757/” pts) Use 1: inition of limit of a se ence tr? €7L+ ' [L that n —> 1 s n —> 00. air; : e )1, have 14.95” Bonus problem (10 pts) Find 35mg (3 + 33:) (9) WW '_ Eryn ’/ . (3&2; flux : ’60“ Lew“ xao’ $9” ) end—t7.) (HJX : Kw!!! Zn??? :_ em/i: 19:0 Z (zap 23m. : anacW/g = @494 20+?) x? )2 907% V90 6777‘s M J. h, n—Byc I 2J2} i. _ ~71 1/249- V5 § I—. ...
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Midterm3v1Solution - Midterm 3 March 22, 2011 (10 pts...

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