102-2003&2004-1-F10-January2004

102-2003&2004-1-F10-January2004 - Kuw Unimflt Math...

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Unformatted text preview: Kuw Unimflt}? :.- Math £92 Jasmin-W 13, 2004 Dept, Math éc Comp Sci Final Examination Duration: ‘2 hours -,._"w—_——H’md——v—wuaw—n——mfi__' I CALCULATORS, MOBILE PHONES AND PAGERS ARE NOT ALLOWED 1. Given that fix) = z + ln(e + tanhx). (9.) Explain why the domain of f is (—00, oo). (1 point} (b) Show that f is one-to—one on its domain (2 point) (c) Show that the ploint P(1, 0} 15 on the graph of f“l and find the equation of the tangent line to *the graph of f—1 at P. (3 points) i i . . dy . 2. (a) Use logarithmic d1fierentiation to find E if 2:0 — i$ + ”5de (3 (int; y (e‘$2+sechr)W p. L" (b) Evaluate iim tan“1 (lnz — sinhzc) (3 points) 1—.00 3. Evaluate the following integrals (4 points each) (a? f 3—”? 1min (b) /(sin:c)ln(sin:c)dz (c)! fL—tan:+:inxdm (d) /2z2 _$+8d:1: cos“ x (32 + 4) .1. 4. Determine: iE:3 1 1 2 _1d2 is convergent or divergent. If convergent, find its value. (3 points) a: 5. Find the area of the region that is inside the graphs of both polar equations 7' = sin9 and r 2 sin 20. (3 points) 6. (a) Find the equation of the sphere whose one diameter has the end points A(5 —3, —2) and B(—1, 1,4). (3 points) (b) Find the equation of the plane that contains P(5, 0, 2) and the line 3 = 4 + 3t, 3; = 3 — 2t, 2 = —-3 + t. (3 points) 1 i..p-. O. CO \ I. H. 23 n a + E}. H.293 EL ARE: ATE. Eamvpnvn+flwarav¢<a .EHE. =:n+fl§ruvm€a_g&=&mo~ EH. Sbaflfiloo o3 3 MART H + ”fl“... v a MS. as a “v H. J HHHoBEHHHm a: T8 03. 12:5. .H. 5 898,25 8 I098”. E 22 n Em u H u. H33 H a. mo HHS w a: :5 mama: am Hi. .8 flH+wflH+nIH H. . IH a.“ .I u HII.c...H.HHn .mIH I .4”... Hymn—Ha mam” w.” HHWLRI: 9H. fi+aIHFIH+ M Ne w. 3 Fe u THHHIH av F _H + z I HimI TfiEEHtH. - «. +39 3 I t: 3.. + E FH: ”$2535” I 38. Ba EHEI HII: :9 “88¢wa 8. E. Emoaumgw E; T... Hi I... ma Is+wml 8 .8 «Ha. ”aficanlmmuwavl «W5 :53? I .H... .HHHHHIHI I I8. .95 :3 EH: HASH ImEHRHI I 35L 5: afiuulmfi: uvvn Im. BIDS w EH. mu...“ HIT H..+H.+HHHHI:IH.+HH.HH hnfluacmmam m. a... . Hfiflflflfi u%%hmm%uwa%%u$§.§u REHERH fig : H Winn—av me n flange 'a... c n 1 name :EEHHHHEHHHRH fl 5 I THHEI I IcimmHHHH: :8: +.%.mmm8maa_a a... n resnmauzflngaw +:. Hangman I Ewan: 3:08p. + :8: I a: IeHHHmH: a: “now“; + H: ESHI 8...."— + 8: + Q EnmeIImewfiHfi... Hmm... H+—memum. H mnngTQNMQmIluaITQ 1i EEZHEQHHHHH“ "Ban.” T. 3: \JIIHEEH in" 3:3 I Iguana?» EL. E: I mg»: + ”HHS + OI H I :3: a“: + m H2235 + OH 5...”... I HHHmufiIT fiuHimHHJSKTEFiH. .H.H......I.H H mu H. QIIH. ._.umflnIu+umfll hummul %Jfl&HIww:_H—|I§I_m+ 0.. Panama: mangofigcmc RHHMHHRH H.~§§EEE§HI anemic u HHS: n CHE m HmmflaIEMquflflIEHEI ET .m m. .25 95.8 E 9.23 and... .93 58323 H.HH :5 =3» “Egan”. i=5 a n o. .I... E. $33.34 an as :5 5... HIE" aim; .HamHHHu 3%" Ha»: ISmmmEmH+gH ICISmhmuum a... 3; >3» “1.31.?” m. E ooufiwn? Ira. EH;Htgmvnnnfiénmfimwufifl 55.3w. $3.135: HTHHFHH a a.+...+..I§+uHHI HT HHHI HH 3 Hana—mgzmoooafifi 0?“. I8. .25 4283!? In. 3 Samuanmmpafi. aging eh I? In. :55...me @596: ass—.5“. H H, H. >E§too§au§muvan Htmu ”3.15.7; a I» H delmw+E€IS+2uIBua Q. madame—Hi u+ne+ulflnc HATE...“IHH....HHHIHH.-....... ......HIHH.-...I...I.I.. a... ”nu". ..g........-._ ”w... .... “WM .---~ CO ...
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