f2-20C-fa2005

# f2-20C-fa2005 - Print Name Student Number Section Time Math...

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Print Name: Student Number: Section Time: Math 20C. Final Exam December 8, 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. (8 Pts.) Find the equation of the plane that contains both the point (1 , 0 , - 1) and the line x = t , y = - 1 + 2 t , z = 3 t . # Score 1 2 3 4 5 6 7 8 9 10 Σ

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2. (8 Pts.) Find the values of the constants b and c such that the function f ( t, x ) = sin( x - bt ) + cos( cx + t ) is solution of the wave equation f tt = 9 f xx .
3. (6 Pts.) Consider the function z ( t ) = f ( x ( t ) , y ( t )), where f ( x, y ) = ( x 2 + 2 y ) 1 / 2 , x ( t ) = e 3 t , y ( t ) = e - 3 t . Compute d dt z ( t ).

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4. (8 Pts.) The function z ( x, y ) is deFned implicitly by the equation z 2 xy = sin(2 y + z ). Compute the partial derivatives ∂z/∂x and ∂z/∂y as functions of x , y and z .
5. (10 Pts.) Reparametrize the curve

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f2-20C-fa2005 - Print Name Student Number Section Time Math...

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