f-20C-sp2003

f-20C-sp2003 - Name TA Math 21C Final Examination Section...

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Name: Section: TA: Time: Math 21C. Final Examination June 10, 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. Find an equation for the plane that passes through the point (1 , 2 , 3) and contains the line x = 3 t , y = 1 + t , z = 2 - t . # Score 1 2 3 4 5 6 7 8 Σ

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2. The position of a particle at time t is given by r ( t ) = h 2 cos t, 3 t, 2 sin t i . (a) Find the velocity at time t . (b) Find the acceleration at time t . (c) Find the angle between the velocity and acceleration at time t .
3. Find the linear approximation L ( x, y ) to f ( x, y ) = ln( x - 3 y ) at the point (7 , 2).

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4. The gradient of a function f ( x, y, z ) at the point (3 , 4 , - 5) is h 1 , - 2 , 2 i . (a) Find the values of the partial derivatives f x , f y , and f z at the point (3

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f-20C-sp2003 - Name TA Math 21C Final Examination Section...

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