A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let x = x(t) denote the amount of new currency in circulation at time t with x(0) = 0. Formulate and solve a mathematical model in the form of an initial-value problem that represents the ”flow” of the new currency into circulation (in billions per day).
What will be an ideal response?
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Find all the first order partial derivatives for the following function.f(x, y) = 
A. fx(x, y) = - 
; fy(x, y) = - 
B. fx(x, y) = - 
; fy(x, y) = - 
C. fx(x, y) = - 
; fy(x, y) = - 
D. fx(x, y) = 
; fy(x, y) = 
Let 
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Use a Riemann sum with four subintervals of equal length 
to approximate the area of R (under the graph of f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals.
?
__________ sq units
?
Repeat previous part with eight subintervals of equal length 
.
?
__________ sq units
?
Compare the approximations obtained in previous parts with the exact area (12 sq units). Do the approximations improve with larger n?
What will be an ideal response?
Evaluate the double integral
?
?
for the function 
and the region R.
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and R is the rectangle defined by 
and 
.
?
A. 8
B. 6
C. 2
D. 3
E. 5
Simplify the expression. If any variables are present, assume that they are positive.
A. (9x3y4)
B. (9x7y8)
C. (9x3y4)
D. (9y4)