Recent content by daniel.e2718

I read that in Devlin's The language of Mathematics. He said that was "very clever." Being young in mathematics, I thought that was beyond clever. It blew my mind a little bit. I'd suggest that book to anyone. I never thought I would read a mathematics book.

OP, did you mean to reverse those...? b|a \; \rightarrow \; b|a^{2} Is certainly true.

This is true. But we are talking about limits, so I figured that that was implied.

DELETED: I posted work to everything. I apologize for not following the guidelines!

Digital signal processing makes uses of poles and the \mathrm{sinc}(x) function. The normalized \mathrm{sinc}(x) function: \mathrm{sinc}(x) = \left\{ \begin{array}{cc} 1 & \text{if} \quad x = 0\\ \frac{\sin(\pi \, x)}{\pi \, x} & \text{if} \quad x \neq 0...

Ahh this. I didn't think about that at all. Then again, de Moivre's formula... But also, cosine is a transcendental function. None of the exact numbers in my original post had infinite series. Is it possible to express the above numbers in an exact form without using transcendental...

They're kinda the same thing... \frac{1}{0} = \infty \sin^2(0) = 0 so \frac{\sin^2(0)}{0} = \underbrace{\frac{0}{0}}_\text{ind.} = \frac{1}{0}\cdot\frac{0}{1} = \underbrace{\infty\cdot0}_\text{ind.} = \frac{1}{0}\cdot\frac{\sin^2(0)}{1} Use l'Hôpital's rule to find the value for this...

I couldn't really think of a good title for this question, lol. Is it possible that a real number exists that can only be expressed in exact form when that form must includes complex numbers? For example, the equation 2 \, x^{3} - 6 \, x^{2} + 2 = 0 has the following roots x_1 =...

Okay, that's what I was looking for. The last time I did anything with proofs was two years ago in 10th grade geometry, and it mostly fill-in-the-blank. Thanks though!

I'm completely stumped. So is my high-school calculus teacher, but he hasn't done imaginary powers for forty-five years. Hopefully somebody can explain this... To clarify, I understand the reasoning between the following equation: e^{i x}=cos(x)+i sin(x) Now, I need to put some things...