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

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

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

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