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Practice Problem Set, L17-22

# Practice Problem Set, L17-22 - Calculus I Practice Problem...

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Calculus I- Practice Problem Set, Lectures 17 - 22, Spring 2011 1. If f ( x ) = x 2 ln( x 3 ), where does f 00 ( x ) = 0? 2. Let a , b , and k be positive constants. If s ( t ) = ae ¡ kt + be kt gives the distance traveled by a particle in t seconds, show that the acceleration of the particle is proportional to the distance traveled. (That is, a ( t ) = C ¢ s ( t ), for some constant C .) 3. Use implicit difierentiation to flnd the derivative of ln( xy ) + e = e xy 2 with respect to x . 4. Find f 0 ( x ) if f ( x ) = tan ¡ 1 ( p x 2 + 1). 5. Use the fact that if y = cos ¡ 1 x then x = cos y , 0 y to prove the formula for d dx (cos ¡ 1 x ). (See notes, Lecture 17) 6. Find the slope of the tangent line for f ( x ) = ( e 2 x +1 ) p x 2 + 4 cos 2 x at x = 0 by using logarithmic difierentiation. 7. Find dy dx at x = 3 if y = (sec x ) tan x . 8. The position function of a particle is s = f ( t ) = t 3 ¡ 6 t 2 + 9 t . (a) Find the time(s) when the particle is at rest. (b) Find each time interval when the particle is moving forwards and backwards.

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