If z=(x+4y)ex+y,x=ln(u),y=v,z=(x+4y)ex+y,x=ln(u),y=v, find
∂z∂u∂z∂u and ∂z∂v∂z∂v. The variables are restricted to domains on
which the functions...
If z=(x+4y)ex+y,x=ln(u),y=v,z=(x+4y)ex+y,x=ln(u),y=v, find
∂z∂u∂z∂u and ∂z∂v∂z∂v. The variables are restricted to domains on
which the functions are defined.
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)
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)
Let U and V be two independent standard normal random variables,
and let X = |U|...
Let U and V be two independent standard normal random variables,
and let X = |U| and Y = |V|.
Let R = Y/X and D = Y-X.
(1) Find the joint density of (X,R) and that of (X,D).
(2) Find the conditional density of X given R and of X given
D.
(3) Find the expectation of X given R and of X given D.
(4) Find, in particular, the expectation of X given R = 1 and of...
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)...
Suppose u(t,x) and v(t,x ) is C^2 functions defined on R^2 that
satisfy the first-order system...
Suppose u(t,x) and v(t,x ) is C^2 functions defined on R^2 that
satisfy the first-order system of PDE Ut=Vx,
Vt=Ux,
A.) Show that both U and V are classical solutions to the wave
equations Utt= Uxx.
Which result from multivariable calculus do you need to justify
the conclusion.
B)Given a classical sol. u(t,x) to the wave equation, can you
construct a function v(t,x) such that u(t,x), v(t,x)
form of sol. to the first order system.
The average value of a function f(x, y, z) over a solid region E
is defined...
The average value of a function f(x, y, z) over a solid region E
is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the
volume of E. For instance, if ρ is a density function, then ρave is
the average density of E. Find the average value of the function
f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid
z = 4 − x2 − y2 and the...