Question

X =
{a,b,c,d,e}

T = {X, 0 , {a}, {a,b}, {a,e}, {a,b,e}, {a,c,d},
{a,b,c,d}}

Show that the sequence a,c,a,c, ,,,,,,, converges to d.

please...

Answer #1

Suppose d and d 0 are both metrics on X and that the metric
spaces (X, d) and (X, d0 ) have the same open sets. Show, the
sequence (an) from X converges in (X, d) if and only if it
converges in (X, d0 ) and then to the same limit.

Let f(x)= a -bx^c + dx^e where a, b,c,d,e >0 and c<e.
Suppose that f(x0)= 0 and f '(x0)=0 for some x0>0. Prove that
f(x) greater than or equal to 0 for x greater than or equal to
0

dX(t) = bX(t)dt + cX(t)dW(t) for contant values of X(0), b and
c
(a) Find E[X(t)] (hint: look at e ^(−bt)X(t))
(b) The Variance of X(t)

1.
a) Find a value of x other than 0 such that the vectors <-3x,
2x> and <4, x> are perpendicular
b) find the domain of the vector function r (t) = <sin (t),
ln (t), 1 / (t-1)>
c) Determine if the sequence converges or diverges, if it
converges determines its limit
ln (2 + e ^ n) / 2020n
d) Find the point (a, b, c) where the line x = 1-t, y = t, z = 1...

Suppose K is a nonempty compact subset of a metric space X and
x∈X.
Show, there is a nearest point p∈K to x; that is, there
is a point p∈K such that, for all other q∈K,
d(p,x)≤d(q,x).
[Suggestion: As a start, let S={d(x,y):y∈K} and show there is a
sequence (qn) from K such that the numerical sequence (d(x,qn))
converges to inf(S).] Let X=R^2 and T={(x,y):x^2+y^2=1}.
Show, there is a point z∈X and distinct points a,b∈T
that are nearest points to...

The general solution of the system of coupled equations d x d t
= 2 x + a y , d y d t = b x + c y can be written as
[ x ( t ) y ( t ) ] = C 1 [ − 1 1 ] e t + C 2 [ 2 2 ] e 3 t.
Determine the values of a = , b = , c
= . Give the values of C 1...

Solve the IVP x''+ax=b+e-ct, x(0)=x'(0)=0, a, b, c
all positive parameters. Does your solution approach a constant as
t goes to infinity? If not, why not?

Given the equation, a(second partial-∂ x/∂ t) + b(∂ x
/∂ t-first partial)+ c x = 0 show that A ⅇⅈ ω t is a solution for
certain values of ω (Be sure to specify all relevant values of ω).
(Begin by substituting x = A ⅇⅈ ω t into the above equation and
then solve for values of ω such that the equation is satisfied for
all values of A and t

Show that E(x,t) = Emax. Cos (kx – wt)
And B(x,t) = Bmax. Cos (kx – wt)
Are solutions to the Wave Equations

Consider the following wave function:
Psi(x,t) = Asin(2piBx)e^(-iCt) for 0<x<1/2B
Psi(x,t) = 0 for all other x
where A,B and C are some real, positive constants.
a) Normalize Psi(x,t)
b) Calculate the expectation values of the position operator and
its square. Calculate the standard deviation of x.
c) Calculate the expectation value of the momentum operator and
its square. Calculate the standard deviation of p.
d) Is what you found in b) and c) consistent with the
uncertainty principle? Explain....

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