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DERIVATIVES II TEST A 2009

# DERIVATIVES II TEST A 2009 - NAME AP CALCULUS DIFFERENTIAL...

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NAME______________________ AP CALCULUS DIFFERENTIAL CALCULUS II TEST A FULL SOLUTION : Answer each question on the LEGAL SIZE paper provided with COMPLETE STATEMENTS when required. 1) ( 4A , 1C ) Let ( ) ( ) x t t t = + + 2 8 1 ln represent the position of a particle in meters on the x –axis with t 0 seconds. Find the velocity of the particle when the acceleration is zero. 2) Evaluate the following limits. Show all your work for full marks. a) ( 2K ) lim cos tan x x x x 0 2 1 b) ( 2K ) lim arctan arcsin sin x x x x 0 3 4 c) ( 3K ) lim x x x x x x x x x + + + + 1 4 3 2 4 3 2 4 12 16 7 2 2 2 1 3) Consider the function ( ) y x = cos arcsin 2 , [ ] x ∈ − 11 , . a) ( 3K , 1C ) Show that ( ) y x = cos arcsin 2 can be simplified to y x = 1 2 2 . b) ( 1K ) Find dy dx in simplest terms. 4) ( 3K , 1C ) Let ( ) f x be a continuous differentiable function such that ( ) f 3 10 = and ( ) f x 4 for 3 7 x . How small can ( ) f 7 possibly be? 5) ( 4K , 1C ) Let ( ) g x
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