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102-2003&amp;2004-1-M20-december2004

# 102-2003&amp;2004-1-M20-december2004 - Kuwait...

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Unformatted text preview: Kuwait University Math 102 . . 7 December 16, 2004 Dept of Math & Comp Sci Second Examination - Duration: 75 minutes ————-———____.________________m________ The use of calculator is not allowed. 'Ihrn off your mobile phone or pager _. (8.) Which indeterminate form does the function (3 — 2tanh zfmhz have as a: —) co, and state why? (1 points) tan :5 sin .7: (b) Find lim z—‘O+ 3" 00522: . , , , ( ), 1f1t emsts. (2 pomts) . Find the partial fractions decomposition of _ m5+2z4+x3—4zz+2 Hz) 1'4 + 2x3 + 2:1:2 (3 points) . Evaluate the following integrals. (3 points each) (a) / (cosh .2) sin 1' d: (by / ———-—-—(GI _ 8 _ \$2); do: sec‘ 3: (c) [mains (d) ch v sinh2 a: — 3 2 t. 5 (e) [Adz 2sinx+2cosx+3 00 1 Does the inte 31 / —————dx conver e or diver e? If it conver es, ﬁnd its value. gr 3 r—-—6I __ 1 g g g 1 (4 points) 00 99 . ' I . . 1. {J — 2tzmhz)3'" '2 hm: the Indetermmzsm form 1"“ as ‘7 —- on since lim (3 — Etauhx) = 3 — 2 lim Lamina: : 3 — 2 2 1. and lim sinhm 2 on. :—m 5"”0‘3 ’“m 3" msa : . { uhz — W has the form 00 — 00 at. G. 11m (1‘ ' : lim (3” _ "him" lim m2rln3 IHU+ hm: 5m .1- Ian 1‘ tim :- x_.0+ see I - r- . i :1 u .w 2 I} 1* i2: 4-:- —4aj 12 2-": -—-l:- , "" 1 +2: +21" z z‘+2z3+2:‘ " and 243—422 _ 2wT"—.1r“ _ A re (‘11:?) , :‘+2:J+2zi _ :r"(:‘+2r+2} _ z + I—‘ + I9+21+2 _ “:3 —412+2:(A+C)m3+(2A+B+D):rQ +(2.:1+QB}2'+EB .4+c=~1 2A+E+D=—4 2A+2B=U 25:2 .r—{I' x+2i+8 z’+2z+2 + (3+0 1“ 1"{1 +2z+2l A: 12-1-2 Haw-2:“ run" '2 A l4; 3 I‘+2:r"+217 — I ‘- :r ' z2 _ r':+2;r+2 3. (a) I = f(cosha:)siz11dz, u : cosh: du : 5111:, du :- 511111 min: 1) = hcosr . . , , 1 = judo =u1rv-jvdu = ~cosllxcosx+fsmham05xdz = wt:05h:c¢:o;~;.x-6-fsml:r(smx} dz = u cosh ICOSI + sinh :1: sin a" — 1 I : —% coshzcos 1‘ + ésinh Li'SiIlI + C (b) f_.ﬁ_.I—E.c11-=/ 'T .amiinésmgf%cu56dﬂ=[(mn 2'50c0—1-35uc20)d (51—8—42): (hm—3):)? =scc0+3tzmﬂ+ C: .IV C lir-ﬁ—z“ ' Ln" 3 (C) j “J I 415 = _/(liu1:r)— 1"3 soc?! 1: surgx til" 2 [mm 37)—”3(1 4’ L""21:)SEC:T(II — n: I '1 ‘ ' ' ‘ ‘ ' u_& I 2 firms“ + new“ : gym + gum” + C : gumwar + tuna/.11. + C '.'u E— In: Huw ("'51 = m: .‘ _ H I \$11) :1 =1un§.da:= ﬁg, 5111.1: : Q-«l—lnn‘,‘ '2 2 4 2n 2 g ‘_ £1“ __ ._. __L_ 7 + + r _ jZHmS-Hﬂi-‘T'Hi [Ll W I"'-i"-’-—~-r"""' +3) I‘M-P'd” u-‘+-m+5d“ 1” [u 4“ J14 C Hu- I1"- =1u|tnnzg+4tmui +5|+C -:' g' ‘ IIECQhIIE If” 11:2m-c0 7_ - I ‘ (‘4) d3: =f ""' T (11' = [7?- = [sec EMU = 111lhl‘.(‘.0 + muf?‘ + C sink" 2—3 cash? x—l 1“ —'l 9 _ =1” (0,3,, + cos: :- 4 + C “gar—1 " _ r—‘. ‘1. u : [ﬂan—“(hi 2212“! I 615—]. c m ._' 1 .._g ' -1 ‘_ _ , “i r z _ I; —l r fmdl—clﬂgo mdAL—chggootln \/()c 1 tan 7r 21m x/J : l O. 99 ...
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