Recent content by fernlund

Yeah, it's correct for all of the examples I can think of. Thanks!

If I have a periodic wave x(t) with half-wave symmetry, it means that: x(t + T0/2) = -x(t) where T0 is the period of the wave. Would this automatically lead to the conclusion that X(t + T0/2) = -X(t) where X'(t) = x(t), i.e X(t) is the integral of x(t). ?

Hello! I have the following problem: Three brothers are aged 6, 10 and 14 years old. Will they ever, in the future, have a prime number birthday the same year? Looking at all of the prime numbers between 1 and 100, it seems that they won't. So I guess this is the same thing as saying: are...

Ah, thank you very much! I've got it from here :)

Hello! So, I'm having a bit of a problem with an exercise in my Calculus book. I'm supposed to find the Maclaurin series representation of $$ \frac{1+x^3}{1+x^2} $$ and then express it as a sum. Am I really supposed to differentiate this expression a bunch of times..? That will be very...

OK, thank you so much! It really means a lot to me that you took your time :) Is it even possible to calculate it as a definite integral in the u-form?

Oh yeah, that's correct! Thank you so much, it was the sign of x that did it. But then I have another question. Actually, what I want to do is calculate the original, definite integral from x = -1 to = 2 which is a bit problematic since the antiderivate which we just calculated isn't continuous...

Well my next step would be $$\d{u}{x} = 2x$$ and x = $$\ \d{u}{x} \frac{1}{2}$$ which would lead to $$\ \frac{1}{2} \int \sqrt{u} du \implies $$ $$\ \frac{1}{3} {u}^{\frac{3}{2}} + C $$ but that's not correct, so I'm still missing something.

Thank you so much. Actually, that's about as far as I've gotten. Then I was thinking I should subtitute u = $$p + x^2 $$ and maybe break out the $$\sqrt{x^2} $$ but that would give me $$\left|x\right|$$ right? Or rather, this is wrong, right? $$\int x \sqrt{p + x^2} $$ I think I'm...

Hello! I need help to integrate the square root of: p x2 + x4 by the method of substitution, p is just a constant. I've been trying for a long time but I can't get it right. I know the answer and it still doesn't help. Thanks! (sorry, I don't know the Latex stuff)