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Unformatted text preview: equation 2 P 2 x + ln( P + x ) + 1 P = 200 (a) Find dP dx as a function of x and P . (b) Find dx dP as a function of x and P . (5) Suppose f ( x ) = ex + sin x . Find f 000 ( x ). (6) Suppose f ( x ) = ln x . Find f 000 ( x ). (7) Calculate the following indeﬁnite integral: Z ( e x + 2 x 2sin x ) dx (8) Calculate the following indeﬁnite integral: Z x 2 e 2 x 3 dx (9) Calculate the following indeﬁnite integral: Z ln( x ) x dx (10) Calculate the following indeﬁnite integral: Z ± e e 2 x e 2 x + x ² dx (11) Calculate the following indeﬁnite integral: Z x + 5 x dx (12) Calculate the following indeﬁnite integral: Z x x + 5 dx (13) Consider the following graph of a function f ( x ): In the spaces below, write either a ’+’ or a ’’ to describe the intervals on which the ﬁrst and second derivatives of f ( x ) are positive or negative. A B C D E f’(x) f”(x)...
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 Fall '08
 KAZEZ
 Math, Calculus, Derivative, dx, following indeﬁnite

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