ex3sol - MTH 133 ~— Seotion 14 ~— Test Three DEPARTMENT...

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Unformatted text preview: MTH 133 ~— Seotion 14 ~— Test Three DEPARTMENT OF MATHEMATICS Michigan State University November 37 2005 NAME: \ {El 9%? {35”} ID NUMBER: SIGNATURE: 1. This exam has 5 pages including this cover. There are 7 questions. 2. Include units in your answers whenever appropriate. 3. You may NOT use your calculator. 4. Sines7 cosines, and tangents of simple angles are to be written out. For example, if you have a C086», you should write 5. Present your solutions to each problem in a clear and orderly fashion. Include enough steps to permit the grader to follow your method. Your method must justify your answer. PROBLEM POINTS SCORE 1 30 2 20 3 10 4 10 5 10 6 10 7 10 TOTAL 100 Present your solutions clearly. 1. (10+10+10 points) Find the following indefinite integrals. (a) fmsinzcdx é)? fiajflgb W y%{“{§3?§) ’ j” {£2ng a fié‘iii’if W “a” Xéégx «% 5665 x agxi M 7<<¢3§§< mfgf‘flfifyc 1 I 5” 3 (b) /_———$(m2+1)dac { Qévir’éw‘g Tm¢hm 5€C§m§3§§f§fia> % A 10+ _ fimva: X{5:6} w 7‘” X24»; €13 ééxzvéwi‘) +(gx1’ig74 "" (3&5) 9:2" fCrfi ‘% 7‘1. Wmhimififi {gégeh‘éwk f} 3"!”{3‘3 1% ii} 8: pg} Si? ‘ I _, jxéxi $52K :1: /:~ ’ b y: x ‘ W} { x m?“ a 53% M '2?! ,3 ' m. ,, w i 5, 7 ~ <c>/x+1dm QM“ gfimixz‘fl> fiwC x2+4 i gm :3“ 51:12:43» {oméfigfig’gmx} Z: i Z?‘ [\3 Present your solutions clearly. 3 2. (10+10 points) Find the indefinite integral 3 x (156, ~1 < a: < 1 / V1 -— 332 ' ’ using the following methods: (a) trigonometric substitution; 6 afiifiv’si 6’? ggiegmg 2‘ W a Swazi»:— jii l, s‘ehfie /’ it in grew-g ; 2"» w ; was: {is} rm; g5»;(z ‘35?! $2: x; ét‘éofieafée j{§’{§§28)¢ gsw'éag iggjwiimfii F Siriwua} ago: ; w Frugal pm '3‘“; CA 3;)r’ré ‘1 fe§§+ées&%< ; W ti 3 w r i ' « \Q ,. ‘ ,L. m, 2 Z 3‘ >< 2» “i” 3‘: 5 ><~ > ii. < (b) back substitution. h” 95%5‘ 52% : Present your solutions Clearly. 4 4. (10 points) Compute the following limit: n , n 11m n—eoo (n + 1) 5“ :53 F”? ' hei/ } e»: Jig/:4 j’m n) m'FQG we; \ ; {fa/V“? V? w fl figw QM 16w :3 Cami, I} 1:: IA m / ‘3 W39") m (to i m <22 we 4’14”? 5.5:“ W may? (“3” 5) ) 5 W :1; {3 1:34 W M J’W’“ fl? {mega W afiw M; 3/;3, .a be an: 9;,5 So it” [53“ r" i may Vic/Mi} ' we we} VC 1 5. (10 points) True/False: @ F Q The function y(t) 2 O is a solution of the initial value problem Suppose f and g are continuous functions and 0 g f 3 9(1’) on the interval [7, 00). Then f7oo f dm converges if f7“) 9(5):) do: converges. fig {3 W 95%??? 569:??? , +5.23% 1 i, /mdx:1“lf<$>‘+0 5e; weddieo If an —* L as n —9 00, then lim ea" : eL_ 71"“)00 €er¢e xiii?) : (3 g {S €5e§§fiv€€m§j We we? arm/see 53>??th é Menage» 3% gvrgc‘hzm 3 2. 55%?“ “35 5:12: {leaéag kmagfi weasel-if s: é‘:’1~«§3}®§€4. %% =3t—y3, 11(0) =0- wm Fiwgfiéé 33 +53 rifle £39? €621??? /, L??? game; 3;??? 3 @ gaffe?“ £53933; SIEEE : no?» giggide Present your solutions clearly. 5 6. (10 points) Use either the limit comparison test or the direct comparison test to determine whether the following improper integral converges. 00 1 d /1 Vas3+1 x fig” 2x fl 7; Kg "gar all "11% {\iwj} U N Z {is} 2 x2 "tar all *sévflafeo} 5;; wry—1w“ % xi,“ 3 :5; £10!” all “7:5 1::wa §§?\¢Q g / , g c;qu w ,.3’ i 7 g a: x‘e it my} (g‘gsl )9 3:2“; pleat? , "K r ; MM?’ 6 "is l («0 latréé‘fl ‘LQYEW; I file: &\§a {wtxvfi/iififi, % whet ‘3 7. (10 points) A hard-boiled egg at 980 C is put in a sink of 180 C water. After 5 minutes7 the eggs temperature is 38° C. Assume that the water has not warmed appreciably and that the temperature of the egg changes according to Newton’s Law of Cooling. How long does it take for the temperature of the egg to reach 20° C? L59?” Tig’} 19$ %&mg> 6%? er? fiw {I if} mgb‘} ( I'm 3 The/fl Newwfig Léiw <3“? {oagflji géagj 5i? ’ ~ r “ ,3; a; k (72. {52> 2, mafia, War—«355 W “W \l W\ WW Wy‘ \l 73% 4t ‘30 Q m “7‘ (“N w v m C(\ is i \fi> JR 7“?“ 7‘” \a § x ‘ e13”? }%i/§~§ "2 <35?ng 'végf '5: 529Eer /_13_dx 2 égfiaé ,,; $(1+fi) E5 :6 ‘t 3;... "be" gm“ :33;%§ ...
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This note was uploaded on 09/27/2009 for the course MATH 133 taught by Professor Wei during the Fall '07 term at Michigan State University.

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ex3sol - MTH 133 ~— Seotion 14 ~— Test Three DEPARTMENT...

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