102-2003&amp;2004-1-F10-January2004

# 102-2003&amp;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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