Recent content by Mathguy15

Hello, I wanted to know why the graph of the hyperbolic cosine function (1/2(e^x)+1/2(e^-x)) looks like a parabola. Is there any reason for this? I suppose the individual exponential functions both go to infinity in a symmetric way... but I wanted a better reason :). Thanks, Mathguy

But the numerator is (1+(.05/n))^20n)-1, which is e^[(.05)(20)]-1=e-1 in the limit, so it has to be a constant (unless I missed something here. I just want to understand it D:)

Here's the deal... I don't understand the limit as n→∞ of [(1+(.05/n))^20n -1]/[.05/n] My Calculus book says that it's supposed to approach {e^[(.05)(20)]-1}/[.05], but the numerator is a constant while the denominator goes to 0 as n→∞. The textbook, by Dr. Gilbert Strang, has similar limits...

I don't know how to answer your question, but I thought that the fact that Raoul Bott, who was one of the greatest mathematicians of the 20th century, got degrees in engineering first would be an interesting tidbit. It was electrical engineering though...

Hm... I think that is broadly true. I think that the mind produces such occurrences after plugging away at the problem while you aren't. However, it is important to note that the breakthroughs often come as a result of much conscious work.

A funny thing happened to me recently... I solved a complicated math problem (for me anyway), and it was almost as if I had no idea of what I was doing. I just started writing... and it kind of came out, unconsciously... I think I know why Poincare said that intuition creates while logic...

Yeeeeeeeeeeeeeeaaaaaaaah

Aw, now what makes you say that?

Oh yes, I think that example is indeed pertinent. I had an algebra book that had a chapter devoted to inequalities, so when I see that problem or others like it, I think AM-GM.

Well, it wasn't completely obvious, or gentle, really. But, now that my mind is oriented the way it should, it's really fun :smile:

Hello, I just wanted to point out a fact obvious to most of you, the fact that: CALCULUS IS AWESOME! That is all, Bye Mathguy

Ugh... this illustrates my point http://www.math.harvard.edu/~knill/teaching/math1a_2011/handouts/27-catastrophe.pdf This page makes absolutely no sense... I might go read a bit of the darn book.

http://www.math.harvard.edu/~knill/teaching/math1a_2011/handouts.html Well uh.. this wasn't necessarily due to HallsofIvy. The notes have definitions that differ from other resources (as HallsofIvy has pointed out before), and the answers to homework problems aren't always there (which is why...

Maybe I should read an online book from Mit Online Courseware. These notes I'm reading through are unclear in places >:(

And, for every M>0, there exists x>M such that cos(x)=0... Graaaaaaaaaaaaaah Calculus!