Recent content by hwmaltby

Oh, you're right! Wow, I feel extremely stupid now. Well, thank you for all this!

Oh, I got it! Thank you for your help. I did it by applying AM-GM to a^2, b^2, c^2, and d^2 and again to ab, ac, ad, bc, bd, and cd. I then added them together. If there is a more elegant way, could you share it? Once again, thank you for your help!

Yes, I suppose I forgot a square root sign... That solves my "quartic" problems.

Hello! I normally consider myself fairly decent with algebra, but when it comes to inequalities... Well, I cannot even solve this very simple one, so please help me! I have been (somewhat) studying inequalities for the past few days, but I cannot find a theorem that deals with changing...

You're welcome =). I generally make new tex tags, but I believe there is a way using \vspace[]. However, you should probably ask someone more experienced than I =).

Oh, yes, I wrote it in tex tags, but it disappeared for some reason =(. I was using mobile physicsforums, so I messed up. It's edited now...

Try using x=4\tan{\theta} :).

Haha.. It's okay =P. It simply means "is equivalent to" and it is used with modulus arithmetic. It's simply syntax because if you write 107=59 \bmod {3} it looks as if you're saying 107=59 which is obviously false. So, the "Ancient Math Gods" decided to write 107 \equiv 59 \bmod {3} to...

Yes, it is more advanced, but it will help prepare you for even crazier ones, such as the Fibonacci Sequence! Another crazy one I managed to do was derive how many triangles there are in increasingly large triangles for a certain side length (f(n) where n was the side length of the equilateral...

Hi! First of all, you said that the sequence of the numbers in the sum 1+2+4+5+6+8+9+7+6+5+3+2+0 differed by alternating 1's and 2's. However, it differs by 1, 2, 1, 1, 2, 1, (-)2, (-)1, (-)1, (-)2, (-)1, (-)2; you have adjacent 1's in two places (4+5+6 and 7+6+5). If I understand you...

Haha.. I felt similar sensations when I proved several of the Taylor Polynomials =P. Congratulations!

Never mind... I rewrote it as: \int \csc{\theta}\cdot\sec^2{\theta} \, d\theta And used u-substition: u=\sec{\theta} \int \frac{\csc{\theta} \cdot \sec^2{\theta}}{\tan{\theta} \cdot \sec{\theta}} \, du \int \csc^2{\theta} \, du \int \frac{u^2}{u^2-1} \, du \frac{1}{2}...

Homework Statement \int \frac {\sqrt {1+x^2}}{x} \, dx Homework Equations \sin^2{\theta}+\cos^2{\theta}=1 The Attempt at a Solution x=\tan{\theta} I simplified it down to: \int \frac {1}{\sin{\theta} \cdot \cos^2{\theta}} \, d\theta Which I do not know how to integrate. Any help would...