Question 1

Evaluate the double integral  for the given function f(x, y) and the region R.  ; R is bounded by  and y = x.

Accepted Answer

The answer of Evaluate the double integral  for the...

Question 2

Evaluate the double integral  for the given function f(x, y) and the region R.  ; R is the rectangle defined by

Accepted Answer

A)  5 
B)  0 
C)  3 
D)  - 5

Question 3

Maximize the function  subject to the constraints  .

Accepted Answer

A)  Max. of  at
 
B)  Max. of -2 at  
C)  Max. of  at
 
D)  Max. of  at
 
E)  Max. of 6 at

Question 4

The annual sales (in billions of dollars) of global positioning systems (GPS) equipment from 2000 through 2006 follow (sales in 2004 through 2006 are projections). Here,  corresponds to 2000.  Find an equation of the least-squares line for these data. Please round coefficients to the nearest hundredth if necessary. Use the equation found to estimate the annual sales of GPS equipment for 2005.

Accepted Answer

A)  $17.91 billion 
B)  $22.66 billion 
C)  $24.23 billion 
D)  $21.52 billion 
E)  $20.93 billion

Question 5

Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function.

Accepted Answer

A)  (8, - 6); relative minimum value: f(8, - 6) = - 24 
B)  (- 8, 6); relative maximum value: f(- 8, 6) = - 56 
C)  (8, 6); saddle point: f(8, 6) = 24 
D)  there are no critical points

Question 6

Maximize the function  subject to the constraint  .

Accepted Answer

A)   
B)   
C)   
D)

Exam 8: Calculus of Several Variables

Evaluate the double integral for the given function f(x, y) and the region R. ; R is bounded by and y = x.

Evaluate the double integral for the given function f(x, y) and the region R. ; R is the rectangle defined by

Maximize the function subject to the constraints .

Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function.

Maximize the function subject to the constraint .