This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: (a) and (b). 3 3. (12pts) Consider the surface deﬁned by the equation f ( x,y ) = x 2 y + y 3 + x . (a)(6pts) Find the tangent plane to the surface at the point (2 , 1 , 3). (b)(6pts) Find all second partial derivatives of f ( x,y ). 4 4. (14pts) (a)(5pts) Find the velocity and position vectors of a particle that has the acceleration vector ~a ( t ) = (2 , cos t, sin t ) , the initial velocity ~v (0) = h , ,1 i and the initial position ~ r (0) = h 1 , 1 , i . (b)(1pt) Find the position vector at the time t = 1. 5 Answer the following two questions in any order. Simplify your answers as much as possible. (c)(4pts) Find the curvature at t = 1. (d)(4pts) Find the length of the projection of the acceleration vector at t = 1 on the unit normal vector at t = 1. 6 5. (3pts) ( Bonus, full credit only) . Show that if a particle moves with the constant speed, then the velocity and acceleration vectors are orthogonal. 7...
View
Full
Document
This note was uploaded on 05/07/2008 for the course MATH 126 taught by Professor Smith during the Spring '07 term at University of Washington.
 Spring '07
 Smith
 Math

Click to edit the document details