# exam23 - f at(3 4 to approximate f(2 8 4 1 3(4 points The...

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Name: Section Number: TA Name: Section Time: Math 10C. Midterm Exam 2 May 20, 2004 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. Consider the function f ( x, y ) = e y 3 x . (a) (2 points) Find all the first partial derivatives of f . (b) (2 points) Find all the second partial derivatives of f . # Score 1 2 3 4 Σ

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2. Consider the function f ( x, y ) = sin(4 x - 3 y ). (a) (2 points) Find the linearization of f at the point (3 , 4). (b) (2 points) Use the linearization of

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Unformatted text preview: f at (3 , 4) to approximate f (2 . 8 , 4 . 1). 3. (4 points) The height of a cylinder is increasing at the rate of 3 cm sec , while its radius is decreasing at a rate of 2 . 5 cm sec . At what rate is the volume of the cylinder changing when the radius is 4 cm and the height is 5 cm? 4. Consider the function f ( x, y ) = cos( xy ). (a) (2 points) Find the gradient vector of f . (b) (2 points) Compute the directional derivative of f at the point (0 , 1) in the direc-tion of the maximum rate of increase of f ....
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