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102-1999&2000-3-M10-July2000(1)

# 102-1999&2000-3-M10-July2000(1) - KUWAIT UNIVERSITY...

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Unformatted text preview: KUWAIT UNIVERSITY Department 01' Mathematics .L'. Computer Sciunce Math 102 Jul},I 1I EODO First Mid—term Exam Duration: T5 ltiiuutas WNW Calculators and mobile phones are not allowed 1i Shaw that figs} =4 1 rln(3:1:) has an iuvcrae. Find f‘1(rtj and state its ' domain and range. [4 pta] 1 Given that ﬁx) = 2::3 + 55c + 31 ﬁnd the slope of the tangent line to the graph of Tim} when m = 10. [3 ptsi 3. Use logarithmic di’ﬁerentiatimi to ﬁnd ftp} , where [3 pits] «in: + 1 SQCEJ ' WU] : —-'.—-“— ’ ‘5 2.1113: 4. Show that: ' [3 phi] tan-1%) = cat—13:, for ail x > i} 5. Prove the identity: [3 {its} ﬂ — cash a + 81111155 1 m tanha " I 6. Evaluate the limit: [3 pts] , .1. iaaiz” + 33% I 7. Evaluate the foilawing integrals: [3 —i— 3 pts} 63—: [8'] 1 + 3'21 a 1 h aim ( 1‘ fr :1: — 4 OO 99 (1} x 3 2‘. = vine- ¥L:}=1‘— Fab-r) s; {furl—- "ﬁ- 5 x 63 £2.“ D£;[OJ H) 91F :t-I O" In) ..I F“; '5‘ =3 Farah-l =3 (atrium. Wg=ﬁrn¢ #:nﬁrm %.€nfrn=g_j " l- '32.: “a =; 1::lr‘E ‘3 "x (9.35"; # I: filLvu—ELE IDF"=E-";'4I,?f 1 -5’ 1 5 gin=u3+5x+i ==J r‘h’r— ”+- J =9 9.2M EGrufgL-{ﬁ‘ I, ”'1 {0:11-r-5’E-1r3 X=fb EGrnp-H 7? (I— II' J'j 5% XJ—"I 3; xcroe 152., y:; e x? *F Pf’hrl') E f Ari“ frJ J}? M 55" (ff—H} .(‘fctaci an}: J—é‘lrxmnﬁ/h 2C” j‘mg uiﬁﬂ- E” I?" I SICK'thI I {:21- ‘7 _ Harm‘- 5:“ _. 1* 5"“ .' i tau: .— afﬁx) \d : EMIJ+ 7" 5 OO 99 ‘ 1 __| :L - '—*-" ft“: 1.1—:- F1 - {14" xi—II 1+3”: x”.- =='J {txlzﬁﬂ+' “r 3‘“ [E_-|' Gall-l ‘— C =3 C = E: .- 1: ': a m an I— I - ﬁ 4' I .J F “(Ia—Ki) {J'L:n ca'fﬁ“ {2L3 59*" & s} ‘“ ’5 — . I .L Ear—ELK {.ij s GM-M [5) LI“: 1mg - :_ mun @wa ”L" ' H . (UL: _ fl ? Cash-rfriLx Cplkﬁ... ﬂair ___,___n—u--|. 311mm 1 'mhxv-ﬁ'm'w mks wﬁ- 3W grub;— mm WM"? ”LI .. CuILat-Irmr‘f .- E'H‘J- ' .—.—.——-— __ _ (5) L- 5'». (2" +3 ):)——g 6 w 1%” £900 £(21+?X) ”a ﬂy... 36-”) X a,” 1”ng " E gaff-n. +9v-3) [43“)H M:Zﬁ’__rﬁ j 2" M" 22%???) H) a 9-1-an _ﬁqg Cb-H KPJD“ . .L £3 éMWJHe :64:- lit-dan- u 99 7- av 6 2M =.)-edX_—d‘4 14.; " ’3 —x I__ e e QIY 3 —JH .. “(L we 1+0?) ”441' , 3 ——l 3 . :_e('tbub\)+C: —-eZa—§’(€TY)+C. . X X“ 4“ 1 A ‘ -1— u =x.._; x=u3.___,3 angu’au ; ’I: H——|————-—-3 ’3’va 1/ 1- g u g. a tr ' 1 :é’; ulna u L134 .2, ~' 64 , 3 at)?“ S." 3 + C i 23 A _l X -; 31“ ('72— )—+ C A; AkJ‘Ln 51.2%va / W “1-?ng :—'==) 2"‘A"‘=“td’ =3 XIJX=23udh ...
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