Test Blog Post

2024-02-03

why its cool

• you can do cool stuff with it (math :nerd:)
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Definition of a Definite Integral

$$\int_{a}^{b} f(x) \,dx = \lim_{n\to\infty} \sum_{i=1}^{n} f(x_i)\Delta x$$

Definition of a Derivative

$$f(x)^\prime = \lim_{h\to0} \dfrac{f(x+h)-f(x)}{h}$$

we love calculus

Vectors

$$\vec{A} = \begin{bmatrix} 1\\ 2\\ 3\\ \end{bmatrix}_, \vec{B} = \begin{bmatrix} 3\\ 4\\ 5\\ \end{bmatrix}_, \therefore \vec{AB} = \begin{bmatrix} 2\\ 2\\ 2\\ \end{bmatrix}$$

Matrices

$$\begin{bmatrix} 1 & 2 & 3 & 4\\ 5 & 6 & 7 & 8\\ 9 & 10 & 11 & 12\\ 13 & 14 & 15 & 16\\ \end{bmatrix}^T = \begin{bmatrix} 1 & 5 & 9 & 13\\ 2 & 6 & 10 & 14\\ 3 & 7 & 11 & 15\\ 4 & 8 & 12 & 16\\ \end{bmatrix}$$

Quadratic Formula

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$ $$when\ ax^2+bx+c=0$$

Boolean Algebra

$$p \implies q \equiv \neg p \lor q$$ $$\neg (p \implies q) \equiv \neg (\neg p \lor q) \equiv p \land \neg q$$