Math_317_December_2008

Math_317_December_2008 - Math 317, Fall 2008, Section 101...

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

Math 317, Fall 2008, Section 101 Page 1 of 2 Final Exam December 8, 2008 15:30 – 18:00 No books. No notes. No calculators. No electronic devices of any kind. The duration of this exam is 150 minutes. There are 10 problems, each worth an equal number of points. Problem 1. (6 points) This problem is about the logarithmic spiral in the plane ~ r ( t ) = e t h cos t, sin t i , t R . (a) Find the arc length of the piece of this spiral which is contained in the unit circle. (b) Reparametrize the logarithmic spiral with respect to arc length, measured from t = -∞ . Problem 2. (6 points) Find the point in the ﬁrst quadrant where the graph of the function y = 1 3 x 3 has maximal curvature. Problem 3. (6 points) Under the inﬂuence of a force ﬁeld ~ F , a particle of mass 2 kg is moving with constant speed 3 m/s along the path given as the intersection of the plane z = x and the parabolic cylinder z = y 2 , in the direction of increasing y . Find ~ F at the point (1 , 1 , 1). (Length is measured in m along the three coordinate axes.)

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.

This note was uploaded on 04/28/2010 for the course MATH 12 taught by Professor Fas during the Spring '10 term at Aarhus Universitet.

Page1 / 2

Math_317_December_2008 - Math 317, Fall 2008, Section 101...

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

View Full Document
Ask a homework question - tutors are online