m2asol-20C-fa2005

# m2asol-20C-fa2005 - Print Name Student Number Section Time...

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Unformatted text preview: Print Name: Student Number: Section Time: Math 20C. Midterm Exam 2 November 21, 2005 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. (6 points) (a) Find the tangent plane approximation L ( x, y ) of the function f ( x, y ) = sin(2 x + 3 y ) + 1 at the point (- 3 , 2). (b) Use the approximation above to estimate the value of f (- 2 . 8 , 2 . 3). (a) f x ( x, y ) = 2cos(2 x + 3 y ) , f y ( x, y ) = 3cos(2 x + 3 y ) , then f x (- 3 , 2) = 2cos(- 6 + 6) = 2 , f y (- 3 , 2) = 3cos(- 6 + 6) = 3 , f (- 3 , 2) = sin(- 6 + 6) + 1 = 1 . Then, the linear approximation L ( x, y ) = f x (- 3 , 2)( x + 3) + f y (- 3 , 2)( y- 2) + f (- 3 , 2) is given by, L ( x, y ) = 2( x + 3) + 3( y- 2) + 1 . (b) The linear approximation of f (- 2 . 8 , 2 . 3) is L (- 2 . 8 , 2 . 3), and L (- 2 . 8 , 2 . 3) = 2(- 2 . 8 + 3) + 3(2 . 3...
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m2asol-20C-fa2005 - Print Name Student Number Section Time...

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