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Gateway Test #1 f'08 key

# Gateway Test #1 f'08 key - '2" = e.otx-L-Sly...

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Pledged. __ --I- ----H _ Gateway Test #1 Math 111 Fall 2007 Please put your answers clearly on this sheet. Check over your work carefully to make sure you have copied your work correctly. If you pass this first test, you will get a bonus of 20 points. You receive 50 points for a perfect paper and 35 points for only one problem wrong. Be very careful. .. For the first four problems, differentiate. Leave your answer with positive exponents and make obvious simplifications (factor). 2 2 --IX 4 1. Y = 9 x - 1 + - - r + 3 Jr (Do not take time to get a common 4 -yx denominator for your answer, differentiate and put as positive exponents.) '2 3 V-a. _.! ~r 9 y. - ';). 1- - -+ -q)( ~l '-/ X ... ~ 3 311 ~ ,,,- /8 X -+ It> X-'I -l- t X • -+ .;;z)<. 0: + 0 /8x+!e + -L +- ~ +0 X Lf g X '/:1. X 3 /:J. 2. f (X) = (cot x) In( cos x) (After differentiating, factor out any common

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Unformatted text preview: ( '2 '\ \,'/ "\ = e.otx. . -L(-Sly\)() + J..rn(C.OSX) -eSc. -x.) -r <. 'X J c.oSX __ CY-atx.-to.n 1-c.:sc.'2. x h(eo~x.) (£(Xl = - \-CSC~'f. .~(eos~ = .:2-)( 3. y[~-1) = C-)(~) X~ "-x-I Gateway Test #1 page 2 5. Y = e-"x-a , where a is a constant. 6. Find the second derivative for y = .J25 -x 2 . Simplify the first derivative before taking a second derivative. lh. j'" (;;)5 -X "-) _l -'X j'= ; (;)S-x~Y(t"XJ--J;lS-X~ I t 'J.J \J~ [ I ~'5-f ~ :\ l \-X "::: (~S-X~) c-(') -(-'f.) _12._(_'2_5_)<2._)_l-6l_X_'lJ ~-J;>S-X'2. + f";}S-X~ ~ (~S-X') (;;}S-j."j j "-;:- :.\ j J_--(~S-X'2.)-X \j'~S;-X~ ("S-X~) 7. Y = x 73' (x + 1) ~ Simplify your answer (common denominator). I 2./3 -'J.h '/3 -.!. iic x 2./3 Li = X . ..L (X+ I) (I) + (X+ /) ,~ X 3 +-J 3 (X+/J2f3 '-= X +~(XT\) ~ 3x '/3 (X -r iy'h 3~ +~ .3x '/Yx +\'(/3...
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