final-practice

# final-practice - MATH 2200 Fall 2009 Practice Final(1...

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MATH 2200, Fall 2009 Practice Final

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(1) Compute the following derivatives: (a) d dx ( x 4 (3 - 2 x 3 - x ) x 3 ) (b) d dy ± e y - sin( y ) y 2 - ln y ² (c) d dt ( sin(sin( e cos( t ) )) ) (d) d ds ± ln s - s s ln s - s ²
(2) Compute the following: (a) Suppose f ( x ) = sin( x ) cos( x ). What is f 00 ( x )? (b) Suppose y = f ( x ) is a function such that 3 y 2 x + 2 xy - sin ( x + y ) = 13 Find d dx in terms of x and y . (3) Consider the function f ( x ) = e x Use linear approximation to estimate the value of f (1 . 1).

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(4) Suppose y = f ( x ) is a function which satisﬁes the equation x 2 - 4 y 3 = 5 and such that f (3) = 1. (a) Find the slope of the tangent line to the graph of f ( x ) at the point (3 , 1). (b) Use linear approximation to estimate the value of f ( 3 + 2 17 ) . (5) Calculate the following indeﬁnite integrals: (a) Z ± 2 x 4 - 2 x + 1 x 2 ² dx (b) Z x sin( x 2 - 3) dx (c) Z e 1 /x x 2 dx
(d) Z 1 5 e 4 t - 3 dt (e) Z (cos( x ) - 3 sin(2 x )) dx

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y is a function of x such that dy dx = 4
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final-practice - MATH 2200 Fall 2009 Practice Final(1...

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