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

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

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;%§ ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern