1694 - MATH 203 Final Exam December 19, 2007 PART I: Answer...

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MATH 203 Final Exam December 19, 2007 PART I: Answer all parts of Questions 1-7. Each question is worth 10 points Question 1 a) Find an equation of the plane that contains both the line x - 1 2 = y - 2 3 = z - 3 4 and the point (1 , 2 , 0). b) Find parametric equations describing the line through the point (1 , 2 , 3) which is perpendicular to the plane z = x + 2 y - 4. Question 2 a) Given the curve ~ r ( t ) = < t, 4 t , t 2 2 > , find a parameterization of the tangent line at (2 , 1 , 8). b) Find an equation of the tangent plane to the surface x 3 z 2 + 4( y - 1) 2 = 5 at the point (1 , 2 , - 1). Question 3 Consider the function f ( x,y ) = x 2 x + 3 y . a) Find the directional derivative of f ( x,y ) at the point P (2 , - 1) in the direction toward the point Q ( - 1 , 1). b) Find the directional derivative in the direction of maximum increase of f ( x,y ) at the point P . Question 4 a) Let R be the region bounded by y = x , y = 2 x and y = 6. Write Z Z R f ( x,y ) dA as an iterated integral. (b) Reverse the order of integration in the integral
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1694 - MATH 203 Final Exam December 19, 2007 PART I: Answer...

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