Let F(x,y,z) = < z tan-1(y2),
z3 ln(x2 + 1), z >. Find the flux of F
across S, the top part of the paraboloid x2 +
y2 + z = 2 that lies above the plane z = 1 and is
oriented upward. Note that S is not a closed surface.
Let
F(x, y,
z) = z
tan−1(y2)i
+ z3
ln(x2 + 8)j +
zk.
Find the flux of F across S, the part
of the paraboloid
x2 +
y2 + z = 28
that lies above the plane
z = 3
and is oriented upward.
S
F · dS =
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find
the flux of F across S, the part of the paraboloid x2 + y2 + z = 29
that lies above the plane z = 4 and is oriented upward.
1. The function f(x, y) = ln(x3 + 2) / (y2
+ 3) (this function is of a fraction format) :
a.
has a stationary point at (1, 0)
b.
has a stationary point at (0, 0)
c.
has a stationary point at (0, 1)
d.
has no stationary points
2. Which of the following functions don’t have unit elasticity
at P = 6?
a.
Demand: Qd = 24 - 2 P
b.
Demand: Qd = 10/P
c.
Demand: log...
Suppose that a firm has the p production function
f(x1; x2) = sqrt(x1) + x2^2.
(a) The marginal product of factor 1 (increases,
decreases, stays constant) ------------ as the amount of factor 1
increases. The marginal product of factor 2 (increases, decreases,
stays constant) ----------- as the amount of factor 2
increases.
(b) This production function does not satisfy the
definition of increasing returns to scale, constant returns to
scale, or decreasing returns to scale. How can this be?
(c)Find...
Let X = ( X1, X2, X3, ,,,, Xn ) is iid,
f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b
< 1
then, find a two dimensional sufficient statistic for (a, b)