1694 - MATH 203 Final Exam PART I Answer all parts of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/29/2011 for the course MATH 190 taught by Professor Ocken during the Spring '11 term at CUNY City.

Page1 / 2

1694 - MATH 203 Final Exam PART I Answer all parts of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online