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Key Gateway 3 f'09

Key Gateway 3 f'09 - )~~~(CDS:J.x to s:l< 4 f(x =...

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Gateway Test #3 Math 111 Pledged-----=K------'-~-- Fall 2009 Please put your answers clearly on this sheet. Check over your work carefully to make sure you have copied your work correctly. 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). 3 5'2 3 3 3 1. Y = 2 X - -3 + -1. - X + J[ (Do not take time to get a common denominator X X 3 for your answer, differentiate and put as positive exponents.) U = ~ ~ ; - 3 'f. - 3 + 3 X '[3_ X S I?- +- 3 tr J :l t.J - "'1 - 3/:L ~' =:. (p'X +Cfx- - X -~ X + 0 _ I 2. q I S 3/~ ~ = l>x -+- ~ --xv] - -; - 2. f (X) = e 2x In( cos(2x)) (After differentiating, factor out any common factors.) \ fl (i) =' e"-Y-. \ (-;;;( sin

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Unformatted text preview: + ;;)~~~ (CDS (::J.x)) to s (:l.)<') 4. f(x) = Arctan(-vX) ~ / { X J =-\. (1-1\-t\ l+~ ;J. . ') Gateway Test #1 page 2 5. Y = In( 2x + a where a is a constant. 2x 6. Find the second derivative for y = , . Simplify the first derivative before (x-l)-1 taking a second derivative. ~ X-!-::lX .::: -x-U I" .eX _1)2(;). .) -~~.;;2 (X-I) -= .:< ~(X-I -::l;)l J (X-IJ~ (X-I)"f. (./= -;:{X-~_ ~"::CX-i)\-J. ..J-(-:l.)<-il'3~ J ( '1.-i)' (X _ r) 'I:,. . 4 j 1/ :: -_ ::l. )( + ':l. + I" )< + ~-: '4 X + rt (X-1J Li &-/)'1 <; , 7. Y = X -3 (X + 1) -3. Simplify your answer. I 513 - Y3 2../ 3 "2/ 3 .~:: X ':C"+ll (I) +-(X+IJ .~ X S jl= _d.XS/~ +-5x7f3(x+J)'-b:: ;;)X /?'+S/6(X+ 1 ) 3CX+i\/3 3 3 (X-tlyI3 ~ I:=. X:l/3 {.;:/ X+-5 ( )\-r il) = X 'Iy 1 X+-5) I 3 (X+lj 13 3 (X+11'13...
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