102-2006&2007-1-F10-Jan2007

102-2006&2007-1-F10-Jan2007 - a» Kuwait...

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Unformatted text preview: a» Kuwait Li’ni'versi'ty Math 102 Date: 15”‘ Januai'yg2007 DeptOF Math & Comp.Sci. Final Exam Duration :2 hours —-——-—-—._._.—_____"__________ 1. {2+2 pts.). Let f(x) = 5057126» -3). :1. Determine the domain off and shoW that f has an inverse. b. Find f" (x) and state the domain of f". (tan hxlm" 2. (3 pts.). Use logarithmic differentiation to Find y' if y = . x > 0. t 3. (3 pts.). Find lim(e"—ll M. .rAO‘ 4. (3 pts. each). Evaluate the following integrals: elm—de b. l——~x2+2x+5dx a] 3H2 --—dx. U; 1.4—1 \MJC—x2 pix (2:2 +1): 5. {4 pts.). Determine whether the improper integral L converges or diverges, and Find its value it' it converges. , 1 I . 6. (4 pts.). Let the curve C: y = —)c2 — In x, x E [1, 2]. Find the area ofthe surface ofrevolution 8 obtained by rotating C about y- axis 7. (3 pts. each). Let the curve F : x =e‘eos! . y :421 sint, te [0,2rtl. . . . . . FT 3. Find the equation ofthe tangent line at the pornt corresponding to I = b. Find the points at which the tangent lines to I" are vertical. c. Find the length of F . 8. (4 pts.). Find the area ofthe region that is inside the graphs of both equations: be» m r=2+2cosi9 and i- :3. SOL U'rfow 3 ‘ 1- 0.. -1 :- 2 X— z. x K \ [8- 3I—T (2) 138.32, <2) xeio) 51%;] .F'OQ:_ 2.3 40) w +9 w oerng :3 {a a) MAW“: =\, age—g 5‘ J-co’a‘Ize‘F-a) $9503:=1Pf-3 => a‘:-"3_(3+cmg)=7x=e"l ———H+m gnu - —4 '~—‘ ‘"' ' A. _ ' z y 18 Cr)- 9% 3+: V— . 5m CDbTéLEX'BJ‘T) Q‘M %1CLe‘—3)=Q=7Pfffofll ‘ — ‘ z-Acfi' —-> €42.)— 2 £43 -(waaafimgx; _ gawfi) x — :1— 3 H F. f }- =7 5‘ + Dec/LDC. 3‘. g:@X_4>HxJ-E| {0M ‘ BEE!) __gi_ K .- W+ ;_ 2 £1,554... ——__..._—.€' _‘f : 6M" : QJ'ML‘ ——-—-—"z”e If” uni-50+ an. 3: AW arr—m} 3540* 61-4 +a‘wm 1' - r ' - :3 1' r ‘ J - r . Hmiczwv‘x - 9*“ (fim’é +£71L)=—3-I- so; ~ x 'L 3 +31: +3 (mm-M5 _ 8. am 52: damw wing) “1' = 3J9. + 4- g (4+ 93593149 "73 ...
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This note was uploaded on 02/23/2010 for the course CAL B 0410102 taught by Professor Deparpment during the Spring '10 term at Kuwait University.

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102-2006&amp;amp;2007-1-F10-Jan2007 - a» Kuwait...

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