practicef2

# practicef2 - Problem 1: If the vectors a and b have lengths...

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

If the vectors ~ a and ~ b have lengths 2 and 9, and the angle between them is π 3 , ﬁnd ~ a · ~ b . ( ) 9 ( * ) 2 ( * ) 0 ( * ) 18 ( * ) 5 . 5 Problem 2: Find the maximum value of the function f ( x,y ) = 2 x +3 y on the surface x 2 + xy + y 2 = 21. ( ) 14 ( * ) 5 ( * ) 19 ( * ) 24 ( * ) 21 Problem 3: Let f ( x,y ) = 4 + x 3 + y 3 - 3 xy . Which one of the following statements is true? ( ) f has two critical points. One is a local minimum and another one is a saddle point. ( * ) f has only one critical point and it is a local maximum. ( * ) f has only one critical point and it is a local minimum. ( * ) f has two critical points. One is a local maximum and another one is a saddle point. ( * ) f has two critical points. One is a local maximum and another one is a local minimum. Problem 4: Suppose z is a function of x and y determined by the equation x + x 2 z + ye z = 3 . Compute ∂z ∂y at the point (1 , 2 , 0). ( ) - 1 3 ( * ) - 1 2 ( * ) 0 ( * ) 3 ( * ) 1 Problem 5: Determine the equation of the plane that contains the lines r 1 ( t ) = h 1 - t,t, 1 + t i and r 2 ( t ) = h 1 + 4 t, 0 , 1 - 3 t i . ( ) 3

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 11/16/2011 for the course MULTIVARIA 251 taught by Professor Staff during the Fall '11 term at Rutgers.

### Page1 / 4

practicef2 - Problem 1: If the vectors a and b have lengths...

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

View Full Document
Ask a homework question - tutors are online