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 () ( ) xt t t =+ + 2 81 ln represent the position of a particle in meters on the x –axis with t 0seconds. 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 xx x 0 3 4 c) ( 3K ) lim x x xxx xxxx −+ −+− + 1 43 2 432 41 21 6 7 222 1 3) Consider the function yx = cos arcsin 2 , [ ] x ∈− 11 , . a) ( 3K , 1C ) Show that = cos arcsin 2 can be simplified to =− 12 2 . b) ( 1K ) Find dy dx in simplest terms. 4) ( 3K , 1C ) Let fx be a continuous differentiable function such that ( ) f 31 0 = and 4 for 37 x . How small can f 7 possibly be? 5) ( 4K , 1C ) Let
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This note was uploaded on 07/27/2010 for the course MATH MATH 1025 taught by Professor Tanny during the Spring '09 term at York University.

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