exam3-practice - equation 2 P 2 x + ln( P + x ) + 1 P = 200...

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Name : MATH 2200, Fall 2009 Practice Exam 3 Please hand only only clearly written work, not scratch paper. Clearly mark your final an- swers for each problem. Partial credit will only be given on problems for which your work is clearly shown. The only allowable materials for this exam are paper, pens and pencils. No notes, textbooks or calculators will be allowed.
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(1) Suppose that x and y satisfy the equation: x y = ln( x ) Find the slope of the tangent line to the graph of this equation at the point ( e, 0). [Hint : the change of base formula for exponential functions is: a s = e s ln( a ) ]
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(2) Suppose that x and y are functions of t which satisfy the equation: 2 x sin( y ) + cos( x 2 ) = 0 Find an equation for dy dt in terms of x and y assuming that dx dt = 1
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(3) A balloon is expanding so that its volume is increasing at a constant rate of 3 cm 3 /sec . Using the fact that the volume is given by V = 4 3 πr 3 , (a) Find dV dr when r = 4. (b) Find dr dt when r = 4.
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(4) Suppose that the price ( P ) and the demand ( x ) for a commodity are related by the
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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 ) = e-x + sin x . Find f 000 ( x ). (6) Suppose f ( x ) = ln x . Find f 000 ( x ). (7) Calculate the following indenite integral: Z ( e x + 2 x 2-sin x ) dx (8) Calculate the following indenite integral: Z x 2 e 2 x 3 dx (9) Calculate the following indenite integral: Z ln( x ) x dx (10) Calculate the following indenite integral: Z e e 2 x e 2 x + x dx (11) Calculate the following indenite integral: Z x + 5 x dx (12) Calculate the following indenite 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 rst and second derivatives of f ( x ) are positive or negative. A B C D E f(x) f(x)...
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exam3-practice - equation 2 P 2 x + ln( P + x ) + 1 P = 200...

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