14. If z=(x+y)ey,x=2t,y=5−t2,z=(x+y)e^y,x=2t,y=5−t^2, find
dzdtdzdt using the chain rule. Assume the variables are restricted
to domains...
14. If z=(x+y)ey,x=2t,y=5−t2,z=(x+y)e^y,x=2t,y=5−t^2, find
dzdtdzdt using the chain rule. Assume the variables are restricted
to domains on which the functions are defined.
Verify the Caucy-riemann equations for the functions u(x,y),
v(x,y) defined in the given domain
u(x,y)=x³-3xy², v(x,y)=3x²y-y³,...
Verify the Caucy-riemann equations for the functions u(x,y),
v(x,y) defined in the given domain
u(x,y)=x³-3xy², v(x,y)=3x²y-y³, (x,y)ɛR
u(x,y)=sinxcosy,v(x,y)=cosxsiny (x,y)ɛR
u(x,y)=x/(x²+y²), v(x,y)=-y/(x²+y²),(x²+y²), (
x²+y²)≠0
u(x,y)=1/2 log(x²+y²), v(x,y)=sin¯¹(y/√¯x²+y²), ( x˃0 )
In each case,state a complex functions whose real and imaginary
parts are u(x,y) and v(x,y)
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.
Two functions, u(x,y) and v(x,y), are said to verify the
Cauchy-Riemann
differentiation equations if they satisfy...
Two functions, u(x,y) and v(x,y), are said to verify the
Cauchy-Riemann
differentiation equations if they satisfy the following
equations ∂u\dx=∂v/dy and ∂u/dy=−(∂v/dx)
a. Verify that the Cauchy-Riemann differentiation equations can
be written in the polar coordinate form as
∂u/dr=1/dr ∂v/dθ and ∂v/dr =−1/r ∂u/∂θ
b. Show that the following functions satisfy the Cauchy-Riemann
differen- tiation equations
u=ln sqrt(x^(2)+y^(2)) and v= arctan y/x.
Consider three binary random variables X, Y, Z with domains {+x,
-x}, {+y, -y}, and {+z,...
Consider three binary random variables X, Y, Z with domains {+x,
-x}, {+y, -y}, and {+z, -z}, respectively. Please use summation
notation
a) Express P(X) in terms of the joint distribution P(X,Y,Z)
b) Express P(X) in terms of P(Z), P(Y|Z), and P(X|Y, Z)
c) Expand the sums from part (b) to express the two elements of
P(X), (P(+x) and P(-x)) in terms of the individual probabilities
(e.g. P(-c) instead of P(C))
Let s = f(x; y; z) and x = x(u; v; w); y = y(u; v;...
Let s = f(x; y; z) and x = x(u; v; w); y = y(u; v; w); z = z(u;
v; w). To calculate ∂s ∂u (u = 1, v = 2, w = 3), which of the
following pieces of information do you not need?
I. f(1, 2, 3) = 5
II. f(7, 8, 9) = 6
III. x(1, 2, 3) = 7
IV. y(1, 2, 3) = 8
V. z(1, 2, 3) = 9
VI. fx(1, 2, 3)...
Find an equation of the tangent plane (in
variables x, y, z) to parametric surface
r(u,v)=〈3u,−5v-5u^2,−5v^2〉...
Find an equation of the tangent plane (in
variables x, y, z) to parametric surface
r(u,v)=〈3u,−5v-5u^2,−5v^2〉 at the point (3,0,−5)
For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of
f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find...
For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of
f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find the unit vectors U+ and
U- , that give the direction of steepest ascent and the steepest
descent respectively.