DERIVATIVES II TEST B 2009

DERIVATIVES II TEST B 2009 - NAME AP CALCULUS DIFFERENTIAL...

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NAME________________________ AP CALCULUS DIFFERENTIAL CALCULUS II TEST B FULL SOLUTION : Answer each question on the LEGAL SIZE paper provided with COMPLETE STATEMENTS when required. 1) Evaluate the following limits. Show all your work for full marks. a) ( 2K ) lim x xx x −− 4 32 2 31 14 4 b) ( 2K ) lim ln cos x x x e ++ 1 1 1 π c) ( 2K ) () lim arctan arcsin sin x x x 0 6 2 2) Consider the function yx = sin arccos 2 , [ ] x ∈− 11 , . a) ( 3K , 1C ) Show that = sin arccos 2 can be simplified to x =− 21 2 . b) ( 2K ) Find dy dx in simplest terms. 3) ( 3K , 1C ) Let fx be a continuous differentiable function such that ( ) f 51 5 = and ( ) 2 for 59 x . How large can f 9 possibly be? 4) ( 4K , 1C ) Let gx be the inverse function to ( ) x x x =+ +− 53 1 . Find the equation of the tangent line to ( ) at the point , . 5) The air pressure Ph at a height of h meters above sea level is modeled by the formula () ( ) e h = 1013 0 000125 . . kilopascals (kPa). An instrument box carrying a device for measuring pressure is dropped into the ocean from a plane and falls in such a way that after
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