MAT016A MT2 W10 Key Temple(2)

# MAT016A MT2 W10 Key Temple(2) - MIDTERM EXAM IISOLUTIONS...

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MIDTERM EXAM II–SOLUTIONS Math 16A Temple-Winter 2010 - Print your name, section number and put your signa- ture on the upper right-hand corner of this exam. Write only on the exam. - Show all of your work, and justify your answers for full credit. SCORES #1 #2 #3 #4 #5 #6 #7 TOTAL:

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1. Diﬀerentiate: (Do not simplify.) (a) (4 pts) y = - x 13 +6 x 2 - 127 73 (Hint: Power Rule) y 0 = - 13 x 12 + 12 x (b) (4 pts) f ( x ) = { sin( x ) }{ cos x } (Hint: Product Rule) ** Note: f ( x ) = { sin( x ) }{ cos ( x ) } was corrected on board during exam***************** y 0 = (cos x )(cos x ) + (sin x )( - sin x ) = cos 2 x - sin 2 x (c) (4 pts) y = 2 x 2 - 3 x 3 +1 (Hint: Quotient Rule) y 0 = ( x 3 +1)(4 x ) - (2 x 2 - 3)(3 x 2 ) ( x 3 +1) 2 (d) (4 pts) f(x)=sin (2 x 2 + 1) (Hint: Chain Rule) y 0 = cos(2 x 2 + 1) 4 x
2. (10 pts) Diﬀerentiate: f ( x ) = tan 2 ( x + x ) x sin x (Do not simplify.) f 0 ( x ) = ( x sin x )(2 tan ( x + x ) sec 2 ( x + x ) (1 - 1 2 x - 1 / 2 ) - (tan 2 ( x + x ))(sin x + x cos x ) ( x sin x ) 2

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3. (10 pts) A population of bacteria is introduced into a cul-
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MAT016A MT2 W10 Key Temple(2) - MIDTERM EXAM IISOLUTIONS...

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