Recent content by Mathitalian

Is N the cardinality of X right? Anyway, I'm quite sure that ##\subset## is used as ##\subseteq##, so 1) holds... You have to check it on your book. If you want, take a look here http://en.wikipedia.org/wiki/Subset#The_symbols_.E2.8A.82_and_.E2.8A.83

Yes, you're right, but if ##A\in G\implies X\setminus A\in G## so, by 3) ##A\cup (X\setminus A)= X\in G ##

Maybe ##\subset## indicate "subset" instead of the symbol ##\subseteq##...

Odd functions of x have only odd powers of x in their Taylor-McLaurin series, so...

First attempt: From ##f(x)-f(a)>0## we have ##f(x)>f(a)## From ##f(x)-f(a)<f(a)## we have ##f(x)<2f(a)## so ##f(a)<f(x)<2f(a)## but ##f(a)<2f(a)\iff f(a)>0\implies f(x)>f(a)>0\implies f(x)>0## Hope this is helpful (and correct xD) [Edit]: I don't have the book

Thank you so much LCKurtz :)

Well.. u(t) is discontinue for t=2 so the Fourier serie converges to [u(2+)+ u(2-)]/2 where u(2+)= \lim_{t\to 2^+}u(t)= 0 u(2-)= \lim_{t\to 2^-}u(t)= 2 so \sum_{k=-\infty}^{\infty}\hat{u}_k= 1 Right?

Homework Statement Let \hat{u}_k the Fourier coefficients of 2-periodic function u(t)=t with t\in [0,2). Evaluate the sum of the serie: \sum_{k=-\infty}^{\infty}\hat{u}_k e^{\pi i k t} for t= 2 Ok, I think there is a trick that I don't know... \sum_{k=-\infty}^{\infty}\hat{u}_k...

Ok, thanks for your hints! So \int_{0}^{2\pi}u^2(t)\mbox{d}t= 12\pi right? :)

Homework Statement Let u(t)=2-\cos(t)+\sin(2t)- \cos(3t)+ \sin(4t) Evaluate: \int_0^{2\pi}u^2(t)\mbox{d}t Homework Equations The Attempt at a Solution Sorry, I don't have any idea :(... As I can see \int_0^{2\pi}u^2(t)\mbox{d}t is similar to the first term of...

Hi whatlifeforme :) You have to use the formula: \int f(x)g'(x)dx = f(x)g(x)-\int f'(x)g(x)dx In this case f(x)= x\implies f'(x)= 1 g'(x)= 5^{x}= e^{x\ln(5)}\implies g(x)=\frac{e^{x\ln(5)}}{\ln(5)}= \frac{5^x}{\ln(5)} so \int f(x)g'(x)dx = f(x)g(x)-\int f'(x)g(x)dx...

or you can use the limit: \displaystyle\lim_{\begin{matrix}f(x)\to 0\\\mbox{when }x\to x_0\end{matrix}}\frac{(1+f(x))^\alpha-1}{f(x)}= \alpha\qquad (\heartsuit) You have just to multiply and divide by c\ne 0 and use (\heartsuit)

Yes, you are right, i have the same feeling. Thank you for your time!

It is a classic exercise on Taylor series :) It is very important to know the macLaurin series of common functions and all the properties of "elementary functions". Practice will help you! :) [Sorry, my English is awful :|]

Thanks for your reply CompuChip :) I can't use numeric integration, but if you tell that this integral can't be expressed in closed form I'll go to my teacher to check it.