Consider the following five utility functions.
G(x,y) = x2 + 3 y2
H(x,y) =ln(x) + ln(2y)...
Consider the following five utility functions.
G(x,y) = x2 + 3 y2
H(x,y) =ln(x) + ln(2y)
L(x,y) = x1/2 + y1/2
U(x,y) =x y
W(x,y) = (4x+2y)2
Z(x,y) = min(3x ,y)
In the case of which function or functions can the Method of
Lagrange be used to find the complete solution to the consumer's
utility maximization problem?
a.
H
b.
U
c.
G
d.
Z
e.
L
f.
W
g.
None.
Consider the following functions
f(x) =x^2, g(x) = lnx, h(x) = cosx
For each of the...
Consider the following functions
f(x) =x^2, g(x) = lnx, h(x) = cosx
For each of the following parts, you may use compositions,
products, and sums of thefunctions above, but no others. For
example, we can combine in the following waysh(g(x)) = cos(lnx), or
g(x)h(x) = lnxcosx, or g(x) +h(x) = lnx+ cosx
show how derivative rules apply to the function you came up
within order to produce the requested derivative.
1)A functionk(x) whose derivative is k′(x) = −tanx=
-(sinx/cosx)
2)...
Let X and Y be continuous random variables with joint
distribution function F(x, y), and let...
Let X and Y be continuous random variables with joint
distribution function F(x, y), and let g(X, Y ) and h(X, Y ) be
functions of X and Y . Prove the following:
(a) E[cg(X, Y )] = cE[g(X, Y )].
(b) E[g(X, Y ) + h(X, Y )] = E[g(X, Y )] + E[h(X, Y )].
(c) V ar(a + X) = V ar(X).
(d) V ar(aX) = a 2V ar(X).
(e) V ar(aX + bY ) = a...
Simplify the following Boolean functions, using K-maps. Find all
the prime implicants, and determine which are...
Simplify the following Boolean functions, using K-maps. Find all
the prime implicants, and determine which are essential:
(a) F (w, x, y, z) = ? (1, 4, 5, 6, 12, 14, 15)
(b) F (A, B, C, D) = ? (2, 3, 6, 7, 12, 13, 14)
(c) F (w, x, y, z) = ? (1, 3, 4, 5, 6, 7, 9, 11, 13, 15)
Consider the vector
field F = ( 2 x e y − 3 ) i +...
Consider the vector
field F = ( 2 x e y − 3 ) i + ( x 2 e y + 2 y ) j ,
(a) Find all potential
functions f such that F = ∇ f .
(b) Use (a) to
evaluate ∫ C F ⋅ d r , where C is the curve r ( t ) = 〈 t , t 2 〉 ,
1 ≤ t ≤ 2 .