. Write down a careful proof of the following. Theorem. Let (a,
b) be a possibly...
. Write down a careful proof of the following. Theorem. Let (a,
b) be a possibly infinite open interval and let u ∈ (a, b). Suppose
that f : (a, b) −→ R is a function and that for every sequence an
−→ u with an ∈ (a, b), we have that lim f(an) = L ∈ R. Prove that
lim x−→u f(x) = L.
Write down a careful proof of the following.
Theorem. Let (a, b) be a possibly infinite...
Write down a careful proof of the following.
Theorem. Let (a, b) be a possibly infinite open
interval and let u ∈ (a, b). Suppose that f : (a, b) −→ R is a
function and that lim x−→u f(x) = L ∈ R. Prove that for every
sequence an −→ u with an ∈ (a, b), we have t
2. Let A = {p, q, r, s}, B = {k, l, m, n}, and C...
2. Let A = {p, q, r, s}, B = {k, l, m, n}, and C = {u, v, w},
Define f : A→B by f(p) = m, f(q) = k, f(r) = l, and f(s) = n, and
define g : B→C by g(k) = v, g(l) = w, g(m) = u, and g(n) = w. Also
define h : A→C by h = g ◦ f. (a) Write out the values of h. (b) Why
is it that...
Write a C++ program to demonstrate thread synchronization. Your
main function should first create a file...
Write a C++ program to demonstrate thread synchronization. Your
main function should first create a file called synch.txt. Then it
will create two separate threads, Thread-A and Thread-B. Both
threads will open synch.txt and write to it. Thread-A will write
the numbers 1 - 26 twenty times in nested for loops then exit. In
other words, print 1 - 26 over and over again on separate lines for
at least 20 times. Thread-B will write the letters A - Z...
1. Let X1, . . . , Xn be i.i.d. continuous RVs with density
pθ(x) =...
1. Let X1, . . . , Xn be i.i.d. continuous RVs with density
pθ(x) = e−(x−θ), x ≥ θ for some unknown θ > 0. Be sure to notice
that x ≥ θ. (This is an example of a shifted Exponential
distribution.) (a) Set up the integral you would solve for find the
population mean (in terms of θ); be sure to specify d[blank]. (You
should set up the integral by hand, but you can use software to
evaluate...
1. Al Einstein has a utility function that we can describe by
u(x1, x2) = x21...
1. Al Einstein has a utility function that we can describe by
u(x1, x2) = x21 +
2x1x2 + x22
. Al’s wife, El Einstein, has a utility function v(x1,
x2) = x2 + x1.
(a) Calculate Al’s marginal rate of substitution between
x1 and x2.
(b) What is El’s marginal rate of substitution between
x1 and x2?
(c) Do Al’s and El’s utility functions u(x1,
x2) and v(x1, x2) represent the
same preferences?
(d) Is El’s utility function a...