Recent content by futb0l

Yeah, the ne^(-n^2) part is actually kind of part of the question. In the question it gives you limits of various functions - I didn't list it here because there is too many. So yeah, basically that term goes to 0 as n approaches infinite.

I think I just worked it out... \lim_{n\to\infty} \frac{ e^{2n} + 1 }{ e^{n^2} + n } \lim_{n\to\infty}\frac{ e^{2n}(1 + e^{-2n}) }{ e^{n^2}(1 + ne^{-n^2}) } \lim_{n\to\infty} e^{2n-n^2} \frac {(1 + e^{-2n}) }{(1 + ne^{-n^2}) } \lim_{n\to\infty} e^{2n-n^2} * 1 So that just equals to 0.

Can you just say that without doing any calculations? O.o

Ok, so then you get: \lim_{t\to\infty} \frac{t^2 + 1}{e^{(\ln{t})^2} + \ln{t}} So basically you will get infinity at the numerator and denominator, which doesn't lead to anything as far as I can see... *sigh*

I meant e^(n^2). So yeah, obviously the one you did with the 't' substitution is not what I'm looking for.

I really haven't got a clue on how to evaluate this limit. I've tried doing algebraic manipulation, but to no avail. (L'Hopital's rule are not allowed to be used). If someone can give me a hint, that would be great :) \lim_{n\to\infty} \frac{(e^n)^2 + 1}{e^{n^2}+n}

Right, thanks a lot :D

Can anyone help me with the following integrals (integrate by substitution)? \int{\frac{dx}{\sqrt{x^2 - 4}}} \int{\frac{dx}{\sqrt{x^2 + 4}}} I have no idea whatsoever on how to do it.

\int{ \frac{x^2}{\sqrt{4-x^2}} } How would I do that? I tried integrating by parts, letting u = x^2 and v' = 1/sqrt(4-x^2) and many other combinations, but I just can't seem to get the result.

Anyways, can anyone help me with this question.. In 1763, the British Admirality covered wooden ship HMS Alarm with copper sheeting to protect it from marine worms. This was successful but, they reported: '... we were surprised to perceive the effect of the copper had upon iron where the two...

Pros: - You wouldn't have to worry about spyware, viruses. - It is fast, and reliable, especially if you're running a server. - Some distros have a really good community. - There are many more that I can't think of right now... Cons: - It's sometimes difficult to get used to Linux (using...

The laws of logs are pretty important and they're pretty easy to understand. \log_{b} mn = \log_{b} m + \log_{b} n \log_{b} \frac{m}{n} = \log_{b} m - \log_{b} n \log_{b} a^n = n \log_{b} a

Lol. I think this is the quickest question ever.

Newton's First Law. The passengers in the car travels with the velocity of the car, but when the car is stopped (by the braking force), the passengers keep going at the velocity of the car because there are no forces stopping it.

Hmm, this might be useful for my aerodynamics stuff...