ef10k

# ef10k - MAC 2313 Dec 7 2010 Final Exam and Key Prof S...

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

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: MAC 2313 Dec 7, 2010 Final Exam and Key Prof. S. Hudson 1) Find the position and velocity vectors of the particle, given that a ( t ) =- cos( t ) i- sin( t ) j , v (0) = i and r (0) = j . 2) Find the directional derivative of f ( x,y ) = 4 x 3 y 2 at P (2 , 1) in the direction of a = 4 i- 3 j . 3) Show that the following is independent of path and compute it: R (3 , 2) (0 , 0) 2 xe y dx + x 2 e y dy . 4) True-False: If D is an open set in R 2 then every point of D is an interior point o f D . If u is a fixed unit vector and D u f ( x,y ) = 0 for all points ( x,y ) then f is a constant function. If f is a differentiable function on the closed unit disk x 2 + y 2 ≤ 1 in R 2 , then f has a critical point somewhere on this disk. If the line y = 2 is a contour of f ( x,y ) through (4 , 2) then f x (4 , 2) = 0. If the graph of z = f ( x,y ) is a plane in 3-space, then both f x and f y are constant functions....
View Full Document

## This note was uploaded on 12/27/2011 for the course MAC 2313 taught by Professor Grantcharov during the Fall '06 term at FIU.

### Page1 / 2

ef10k - MAC 2313 Dec 7 2010 Final Exam and Key Prof S...

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

View Full Document
Ask a homework question - tutors are online