Consider the function f(x,y) = e^xy and closed triangular region
D with vertices (2,0), (0,2) an...
Consider the function f(x,y) = e^xy and closed triangular region
D with vertices (2,0), (0,2) an (0,-2). Find the absolute maximum
and minimum values of f on this region.
Consider the function f(x, y) = 3+xy−x−2y. Let D be the closed
triangular region with vertices (1, 4), (5, 0), and (1, 0). Find
the absolute maximum and the absolute minimum of f on D.
Consider the production function Q = f(x,y) = xy^2.
(a) Totally differentiate this production function.
(b) While holding output constant, solve for dy/dx. What is the
economic interpretation of this term?
(c) Differentiate once more with respect to x solve for d
dx(dy/dx). What is the economic interpretation of this term?
(d) Evaluate the marginal products. Are they positive?
Diminishing?
(e) Evaluate the convexity of isoquant. Does it or does it not
contradict with the properties found in previous part?...
Consider the function given as example in lecture: f(x, y) = (e
x cos(y), ex sin(y)) (6.2) Denote a = (0, π/3) and b = f(a). Let f
−1 be a continuous inverse of f defined in a neighborhood of b.
Find an explicit formula for f −1 and compute Df−1 (b). Compare
this with the derivative formula given by the Inverse Function
Theorem.
1. Find absolute max and min of f(x,y)=
x^2- xy + y^2 +1 on the closed triangular plate in the first
quadrant x=0, y=4, y=x
2. Given position of a particle by π (t)= Cos2ti + 3
sin2ti, Find the
particle velocity and acceleration at t=0
Consider the economy described by the production function
Y = F (K, L x E) = Kα(LE)1-α
(a) Derive per effective worker production function.
(b) Assume there is population growth rate, depreciation rate
and technology growth rate.
-Write the law of motion of k.
-Tell how k* will be changed when population growth rate
increases with graph.
(c) Calculate steady state equilibrium.
k∗ =
y∗ =
c∗ =
(d) Calculate gold rule capital stock and output.
kgold =
ygold =...
Let f(x, y) =x^2+ 3y^2−2x−12y+ 13 on the domain A given by the
triangular region with vertices (0,0),(0,6), and (2,0).
Find the maximum of f on the boundary of A.
Consider the region bounded between y = 3 + 2x - x^2 and y = e^x
+ 2 . Include a sketch of the region (labeling key points) and use
it to set up an integral that will give you the volume of the solid
of revolution that is obtained by revolving the shaded region
around the x-axis, using the... (a) Washer Method (b) Shell Method
(c) Choose the integral that would be simplest to integrate by hand
and integrate...
Let ∬[a,b]×[c,d]f(x,y)dA denote the integral of f(x,y)over the
region with a≤x≤b and c≤y≤d. Find ∬[0,1]×[0,1]f(x,y)dA given the
following: ∬[0,1]×[1,5]f(x,y)dA=2, ∬[1,2]×[0,1]f(x,y)dA=−1,
∬[1,2]×[1,5]f(x,y)dA=4, and ∬[0,2]×[0,5]f(x,y)dA=3.
Group of answer choices
2
-2
8
0
None of the above.