Key Gateway 1 f'09

# Key Gateway 1 f'09 - sec 2,x k(s\~X s)f'X.Lv X ~x 4.2)C ~...

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~ Pledged __ ~-. ..-_--+t- _ Gateway Test #1 Math III Fall 200 0 Please put your answers clearly on this sheet. Check over your work carefully to make sure you have copied your \\lork correctly. Ifyou pass this first test, you \viII get a bonus of20 points. You receive 50 points for a perfect paper and 35 points for only one problem \vrong. Be very careful. . . For the first four problems, differentiate. Leave your answer with positive exponents and make obvious simplifications (factor). 4 -IX 2 l~ Y == 4.. x 3 - - + - C + 7lX (Do not take time to get a common x 3 2 '\I X del10111illator for YOt1r allswer, ditIerel1tiate alld Pllt as positive expOl1ellts.) 3 3 '/2. ... ,/: ~= L{~ -4x- +~X -;lX :l+rr:x I '2. . '1 - Y - 3/2- ~ == I ';;l ~ + I;;" X- -I-. .L X 2.+ X + 11 I . .. " :&. J~ -L ~ - I ~)( +- --;:;. ... ala + X 3/::1. + \ \ 2. f(x) == (tan x) In(sin x) (After differentiating, factor out any common faC;~( Xl == fta.~1 .' · (!. .o5 X'\ +- sec 7.. x Lv. ( '5; () x) ~ 5 ll'\)(. ') ~ (zaY\ y.) c~.sX\

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Unformatted text preview: +sec. 2 ,x. k(s'\~X) s )f'X ) -;; .Lv-. . X ~x + 4 -.2)C ~)( 3. -::: -X (-:J. .X+4j2. . X;-:J -x~)< ~~ (~;-';lJ'). (;2)<. + l/)' 1.. }'==--Cc2: +4)~ Inx 2x+4 Gateway Test #1 page 2 5. Y = sec(2x+a), where a is a constant. ~ '= u.c.C:L)<.+~) ia n0.x +0.) (~') [ ~ I = ~ /1Le-(~X +a.)-tQ.n C;tx+a.) 1 2 6. Find the second derivative for y =-Jl-x . SimplifY the first derivative before taking a second derivative. I I J ( . 2-"-';., :'\ IA :: ~ 1-)(. / l-~XJ =::. _ -~ .J \}I-X~ _, 1/ = (/_X:&.jV 2 (_\j -(-X)~('-X~)i-(-jX) ~ (1-X 7L ) " _X '2. .... (2,) 'J. J. L..\ :. -~ I -~ ;:---1-X-I' _I _ J \jf-X?--=: \j J-X'2-(1-X2-) (/-X~) _ -/TX2.-X~.:: _ I 2' -(I _X-.)?J/ 4 (1-"f. 2.)3/2-7. Y == x 73 (x + lyl3 SimplifY your answer. I 2/'3 - -~ 'I'--3 L.i =-X · 1.. ( ~ + \) 3 + (X + lJ · 3. X -' J 3 3 ~I '13 t -=: X 3 -+ ;;{ ( X + \1 ~ 3(Xf-\j:l-{3 '3X'13 X-+~X+-~ 3 X '/3 (X rlJ~/~ I=. 3~+-~ lj 3; Y3 (X +-\~~/'3...
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## This note was uploaded on 12/05/2011 for the course MATH 111 taught by Professor Bang during the Fall '08 term at Emory.

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Key Gateway 1 f'09 - sec 2,x k(s\~X s)f'X.Lv X ~x 4.2)C ~...

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