Ok, I can plot a single polynomial easy enough such as 3*(x^2)-1 using fplot, but I want to graph multiple polynomials.
When I try to use the plot it doesn't work even for one though. The graph is completely wrong.
ie I make a new m-file.
x = [-1:1];
y = 3*x.^2 - 1;
Then call the...
Homework Statement
Let f be a Lebesgue integrable function in the interval [a,b]
Show that:
lim integral from a to b (f(x)*|cosnx|) = 2/pi * integral from a to b (f(x))
n->infinity
Homework Equations
Every measurable function can be approximated arbitrarily close...
Homework Statement
Let H be an inner product space.
Let T:H->H be a linear, self adjoint, positive definite operator.
Fix h in H and let g = T(h) / square root (1 + (T(h),h)). for h in H
Show that the operator S:H->H defined by S(v) = T(v) - (v,g)g for v in H is positive definite...
Not a true homework question, but I'm trying to find all subgroups of S4.
Including the identity and the group itself, I've found 30. Is that correct?
I've got groups such as:
trivial
s4
alternating group
{identity, (12)}, {identity, (13)} etc - 6 of these
{identity, (123), (132)}...
Regarding the definition of homemorphism, when we say a function is a homeomorphism if it is continuous, bijective, and has a continuous inverse I assume that means over the codomain only.
For example if we have a map from f: R -> (0,1) does f inverse need to be continuous on (0,1) only?
Homework Statement
Let f(x) = integral [x to x+1] (sin(e^t)dt).
Show that (e^x) * |f(x)| < 2
and that (e^x) * f(x) = cos (e^x) - (e^-1)cos(e^(x+1)) + r(x) where:
|r(x)| < Ce^-x, C is a constant
Homework Equations
integration by parts
The Attempt at a Solution
Well...
Homework Statement
Suppose f >= 0, f is continuous on [a,b], and {integral from a to b} f(x)dx = 0.
Prove that f(x) = 0 for all x in [a,b]
Homework Equations
The Attempt at a Solution
Suppose there exists p in [a,b] s.t. f(p) > 0.
Let epsilon = f(p) / 2 > 0.
The...
Let I = [0,1] be the closed unit interval. Suppose f is a continuous mapping from I to I. Prove that for one x an element of I, f(x) = x.
Proof:
Since [0,1] is compact and f is continuous, f is uniformly continuous.
This is where I'm stuck. I'm wondering if I can use the fact that since...
I did.
The problem is if f ' (x) = |x| then f '' (0) does not exist, but neither does:
lim [f (0 + h) + f (0 - h) - 2 f (0)] / h^2, unless I am missing something here???
h->0
I tried both absolute value of x and square root of x and still get 0/0 or if I apply l'Hopital's Rule I get infinity. Which also means the limit does not exist.
Suppose f is defined in a neighborhood of x, and suppose f '' (x) exists. Show that:
lim [f(x+h)+f(x-h)-2f(x)] / h^2 = f''(x).
h->0
Show by an example that that the limit may exist even if f '' (x) may not. (hint: use lHopital's Theorem).
Proof:
f '' (x) exists implies...