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exam2 - z = f x y at the point(1 1(b(2 points Find the...

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Name: Section: TA: Time: Math 10C. Midterm Exam 2 May 21, 2003 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 ) = cos( x 2 y ). (a) (3 points) Find all the second partial derivatives of f . (b) (1 point) Determine whether or not f is a solution to Laplace’s Equation, u xx + u yy = 0. # Score 1 2 3 4 Σ
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2. Consider the function f ( x, y ) = xe xy . (a) (2 points) Find an equation for the plane tangent to the surface
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Unformatted text preview: z = f ( x, y ) at the point (1 , , 1). (b) (2 points) Find the linear approximation of f (-. 1 , 1 . 1). 3. (4 points) Let z = cos( x ) e y , with x = s 2-t 2 , y = st. Use the Chain Rule to find ∂z ∂s and ∂z ∂t . 4. Consider the function f ( x, y ) = ln(3 x + 4 y 2 ). (a) (2 points) Find the gradient vector of f . (b) (2 points) Compute the directional derivative of f at the point (-1 , 1) in the direction of the vector h-12 , 5 i ....
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