I am not sure what you are trying to say here??
1) There exists an x and then P(x) results in M(x)? You say something more about x in order to use these symbols. Like there (\exists x \in A(x) \Rightarrow A(x) \mapsto M(x)
I agree...
I have been away for a while but I think it could be that the young man is suppose re-write the sum to an improper integral and thereby finding the sum of the series??
Homework Statement
I have the heat equation \frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2}
where u(x,0) = f(x) and f(x) = \frac{sin(x)}{x}
use the expression of the Fourier Integral to calculate u(x,t).
Homework Equations
The Attempt at a Solution
Do...
Oh well, I am sure that Jedi Hal will find this post and correct us all, but that said
I learned in High School x^{-1} = \frac{1}{x} which implies
e^{-x} = \frac{1}{e^x} thus
e^{-ln(x)} = \frac{1}{e^{ln(x)}} = \frac{1}{x}
Use this property to prove you problem, OP!
Homework Statement
I am getting fooled by the this improper integral
\int_0^{\infty}\frac{cos(x)+sin(x)}{1+v^2}dv = \pi \cdot e^{-x}
How the devil do I go about getting that result?
The Attempt at a Solution
I end up getting the sum of the two integrals...
I think that you can do it like this:
If you view these two function as series
e.g. \sum_{n=1}^{\infty} ln(n) and \sum_{c=1}^{\infty} n^c and then use the comparison test from Calculus to show that
ln(n) < n^c
You are right :)
a_1, a_2, \cdots a_n are row in the matrix A. I also forgot to mention for this be allowed then A and B must live up to the row column rule :)
It sure was Hall, but I had a feeling that original poster didn't know that
if you have (a+b)(a+b)= a^2 + ab + ab + b^2
It hard to be young these days!
HallsofIvy,
I know you have the ability to use the force at a higher level than the rest of us.
But the assigment does say
"Show that if AB = I, then also BA = I, so A and B
are invertible."
In my opinion it all comes down to how you read the problem at hand.
1) For A and B to...