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# Exam3BSolutions - Name 50mm! 0N5 March 18, 2008 Math 133...

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Unformatted text preview: Name 50mm! 0N5 March 18, 2008 Math 133 —— Hourly Exam 3B Do all problems (Total = 100 points). Show all work. Calculators are not allowed. (1) (a) (6 points) Write out the partial fractions decomposition of the following expression but DO NOT SOLVE for the coefﬁcients A, B, . . . _x_-1__ z A * B + C ,r 2., (iv - 3W3?2 — 1) x~ 3 (x—3Y’ ‘x-\ x+\. 3““ .(i‘C‘bY‘5 0L5 (x-ﬁbu-l) 2 _ (b) (16 points) Use partial fractions to ﬁnd I = / 223%; dry. DCYW = %(%1*"\) “MA Xz-¥L\ fo¢Avcxihi¢ Sa‘ncz. bL’L‘ac. -" O”'L<O w" c 52%» x — 8 A BM. Aim) + (8w. x M = —--—--F ——-;:-—_ “‘— . 2- x x H , ,, xba m3 ngwuon&wam. 55+va M3\-(,\\ “vow/waivers ‘- QKL+X’8 Marc-k cqu w %A*B:l c: 3:; HA=' ml Lice-Ll o : —"'" l ., 1 x M a ’Q'Q’x : “Q. QMl’Xl + 8 \$6444 A”. n l, , . .23. =-' *2 lex\ + 18%” ‘* 1 “W549 ~= -.1 QMM % l limbéﬂ '* 1; mohwk‘é—l *C’ oil =‘\ (its? 4 J3: moi?“ (E) + Q, \! (2) (10 points) Evaluate the improper integral I = /0 Haikde FDG "Be, (“AG/gnilt. ‘Mi-e¢a\ ‘1 Le) RIM-XL du=4x<L¥ iku:xé’¥ "x4x_iiciu_gz~z _-1,~‘__:_\_‘___\ SQW‘Y‘ 18w - 7-8“ CL“ ‘ ‘9‘“ W a 94m?) , L L V x _ .—. ‘ . 3 X ‘ l x -- i ‘ ’ J __l___.1 ’ __ :0 i : U (Airy; ‘ \vi (1U +76.) ‘ 9‘ LIE/Lo |+L 1 + 0 L390 (3) Determine whether the following integrals converge or diverge. DO NOT EVALUATE. Justify your answers using the Comparison Test (CT) and Limit Comparision Test (LCT). \ K ( a)(8 ts) Iz/OouL u (a _ \ p 1 \/\$(2+£E) COIN/“Vaq-e, "\$55) : m (4-H 31X) 2 “x ‘\~ £91 um ‘ 14/; :LJMFF’_L«M<¢(_\ «9 3a.: 3w.) ~= x600 \lﬂLW) XAN XUA-y.) ‘ “A” szli .. u (b)(6 pts) [2/0 E— dzr. m. A“ {i . " X FOR 1: Oi ¥\$\ (pd. \havc. £ e 5.0 EL. 3, ’6‘," A‘x‘eraé o X \ 6" so 301 Ahanécs £2 "HQ, CT ' e QM»: Cii‘igaf’s La ‘iﬁa CT. a °° \ i Vera-es 30 S ) e d (4) (14 points) Solve the differential equation ﬂ d—y = 3/2 with the initial condition y(0) = 1. Seemk Vagka 2 1:; (33 = d“ 2:? in'A’ial COAA‘A-Tﬁﬂ ‘. X=O) ¢8=l ==l> ”\ z '2‘]? + C” Solve ger- a ‘. (5) (8 points each) Calculate the limit of the following sequences. Show all steps clearly. ‘2 ﬂwlgﬂu V}? l = Q“ lift (will l i. (b) lim {7271—1 = (min (Sax-ﬁlm : LN“ €W(9~n—) n n——>oo haw “A” = a (rite M23342 Q/mlc’lxell 73 W 2 6 Kb)” )4 l ~1 sin n (c) If an: R2 What is 3:12am? Sham, ‘-l \$ \$a‘n n 5 . _\ . \ M Ma“ “" 5 5““ n 5 TV a“ h. W n“ . \ — _ W‘ . ‘7‘ (80* \J-NV‘ KL " O CMAA LUV“ T. 3 D So LL...“ ELTYTE- : O \vx->oo “*0 ) We“ ‘Ww, mow-cm. (6) (8 pts) (a) Does the inﬁnite geometric series §+1+1+1+ 4 4 12 36 converge or diverge? If it converges, what is the sum? Justify your responses. 1‘; . , _ _ 3‘ _i__ is V) (L \${qﬁg5 Loriﬁ A — A WA r: 3 5km. IH < \ ‘Ekis Series Cenmées . We 9.0% is A in; ,1“? Vigil) x—r: ﬂ 1-73 “I /3 H’1 8 (b) (8 pts) Write the repeating decimal 0.? as a geometric series. Then write the sum as a fraction. “ 7 0.7: .37 37 37..“ 2 €33)“; 37 4§l§+ﬂ ico‘ lea mi: ;” 6‘ XONFA'VN» sank; “5+6! A337/00 “V‘Cl Y‘ :I—oo : “Cw—e. .— A_§_1“ :§l.,ii:§,mi°_<2 :- ]-Y- ‘ loci 1"!" ’00 ioo [00 ‘7‘? a log ...
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## This note was uploaded on 05/12/2008 for the course MATH 133 taught by Professor Wei during the Spring '07 term at Michigan State University.

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Exam3BSolutions - Name 50mm! 0N5 March 18, 2008 Math 133...

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