Hi,

Here I have three problems I can't get solved no matter what I try. Truthfully I don't have a clue on how to begin. Hopefully someone here is able to help me! All other homework in the course was handed in a long time ago..

Any help is appreciated!

1. Examine the integral of e^(-x)^2 from 0 to infinity.

2. Prove the inequality 1 + ln(x+sqrt(1+x^2)) > sqrt(1+x^2), 0<x<1

3.

P = [1-a a

b 1-b]

S= [-a a

b -b ]

a) show that S^n=k^(n-1)*S, n>2, k=-(a+b)

b) show that P^n=I+((1+k)^n-1)/k*S, where I is the identity matrix.

I'm sorry, don't know how to use that fancy latex-code for the symbols!