why does double rounding 9.46 give 10 but "regular" rounding gives 9?
What's the correct way to round, or estimate, a number to a specified precision? Starting with wikipedia: Rounding a number twice in succession to di...
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Sketch curve $r(t)=\cos t\hat{\bf i}+\sin t\hat{\bf j}+t\hat{\bf k}$
This is from "Multivariable Calculus, Concepts and Contexts" by Stewart. He says "The parametric equations for this curve are: $x=\cos t$, ...
Elementary factors in the Weierstrass Factorization Theorem
Weierstrass Factorization Theorem allows representing an entire function $f$ (can be considered as an infinite polynomial) as a product involving zeros $\...
Is the uniform boundedness principle not trivially obvious?
I read that the uniform boundedness principle is one of the big theorems in functional analysis. However after looking at it, I'm not sure what is so...
What is the inverse function of $\ x^2+x$?
I think the title says it all; I'm looking for the inverse function of $\ x^2+x$, and I have no idea how to do it. I thought maybe you could use the ...
Congruency and Congruent Classes
so studying for my midterm on Tuesday (intro to abstract algebra). The topics on the exam are Division Algorithm, Divisibility, Prime Numbers, FTA, Congru...
How do I find parity check matrix if generator matrix can't be written in standard form?
$G=\left ( \begin{matrix} 1 &1 &0 &1&0&0&1\\ 1&0 &1 &0&1&0&1\\ 0&1 &1&0&0&1&1 \end...
Augmented Lagrangian
Consider the following equality constraint minimization problem: minimize $\text{ }f(x)$ subject to $Ax=b$ Its Lagrangian is then: $L(x,y) = f(x) + y^T(Ax...
Suppose $x$ and $y$ are inversely proportional, if $x^p$ and $y^q$ are also inversely proportional, then how must $p$ and $q$ be related?
Suppose $x$ and $y$ are inversely proportional. Then we have $xy= k_1$, $x=\frac{k_1}{y}$, $y=\frac{k_1}{x}$. (a) If $x^p$ and $y^q$ are also inversely pr...
Compound interest derivation of $e$
I'm reviewing stats and probability, including Poisson processes, and I came across: $$e=\displaystyle \lim_{n\rightarrow \infty} \left(1+\frac{1}{n}...
