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17A Practice Final F2010

17A Practice Final F2010 - 17A Practice Final Fall 2010 2 x...

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17A Practice Final Fall 2010 1. Differentiate: a) y = x x 2 + 3 e sin x b) f ( x ) = ln 2 ! x x 2 " # \$ % 2. If f ( x ) = x ! cos( x ) find d dx f ! 1 ( ! 1) 3. The radius of a circle is measured with a relative error of 5%. What will the relative error be if you use this measurement to calculate the are of the circle? 4. A cylindrical cell characterized by radius r and height h is to be enclosed in a membrane that has a given constant surface area of 12 ! . Find the r and h that maximize the enclosed cell volume. 5. Consider the reaction A + B ! K If y represents the amount (in mols) of A at time t, x represents the amount of B (in mols) at time t, and z represents the amount of K (in mols) at time t. The reaction rates can be modeled by: e y 2 + xy = z . If the amount of A is increasing at 5 mol/min and the amount of B is decreasing at 3 mol/min, how is the amount of K changing when there are 10 mols A and 5 mols of B?
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