102s05fin

# 102s05fin - be the lines whose parametric equations are L 1...

This preview shows pages 1–8. Sign up to view the full content.

B U Department of Mathematics Math 102 Calculus II Date: June 2, 2005 Full Name : Time: 15:00-17:00 Math 102 Number : Student ID : Spring 2005 Final Exam IMPORTANT 1. Write your name, surname on top of each page. 2. The exam consists of 8 questions some of which have more than one part. 3. Read the questions carefully and write your answers neatly under the corresponding questions. 4. Show all your work. Correct answers without suﬃcient explanation might not get full credit. 5. Calculators are not allowed. Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 total 25 pts 25 pts 25 pts 25 pts 25 pts 25 pts 25 pts 25 pts 200 pts 1.) Find the point(s) on the surface xy - z 2 = 1 closest to the origin.

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

View Full Document
2.) Evaluate R (3 , 5 , 0) (1 , 1 , 2) yz dx + xz dy + xy dz .
3.) Let F (x,y,z) be a vector ﬁeld with continuous partial derivatives. Show that div (curl F) = 0 .

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

View Full Document
4.) Evaluate R 1 0 R 1 - x 2 0 5 p x 2 + y 2 dydx .
5.) Let L 1 , L 2

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: be the lines whose parametric equations are L 1 : x = 1 + 7 t, y = 3 + t, z = 5-3 t L 2 : x = 4-t, y = 6 , z = 7 + 2 t . Find the distance between the two lines. 6.) Let a curve in the plane be parametrized by x = 2 t, y = t 2 . a) Find the curvature function of the curve. b) Find the tangential and normal components of the acceleration of a particle moving on this curve. 7.) Evaluate the line integral H C y 2 dx + x 2 dy , where C is the square with vertices (0 , 0) , (1 , 0) , (1 , 1) and (0 , 1) oriented counterclockwise, using Green’s Theorem and then check your answer by evalu-ating it directly. 8.) Find the volume of the solid enclosed between the surfaces x = y 2 + z 2 and x = 1-y 2 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

102s05fin - be the lines whose parametric equations are L 1...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online