Markdown Test

Hello, world!

Go home.

Seriously. go home. Please.

Seriously. go home. Please.

What about “quotes” you say? I don’t know–maybe not–can we find out… Like ‘quotes’ or just “quotes?”


Heading 1  

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Markdown Test  

So $\begin{bmatrix}0 \\ 2\end{bmatrix}, \begin{bmatrix}1 \\ 7\end{bmatrix}, \begin{bmatrix}2 \\ 12\end{bmatrix}$ , and any other points on that line, are all possible solutions to this matrix equation.

  1. If we set the current to any other value $x$ , the voltage across the two terminals will be along the straight line connecting those two points on the V-I plane:
    $$\begin{align} V_{A B} (i=x) & = \text{OCV} \big( 1 - \frac {1} {\text{SCC}} x\big) \\ V_{A B} (i=x) & = \text{OCV} - \frac {\text{OCV}} {\text{SCC}} x \end{align}$$

Or on its own:

$$\begin{align} V_{A B} (i=x) & = \text{OCV} \big( 1 - \frac {1} {\text{SCC}} x\big) \\ V_{A B} (i=x) & = \text{OCV} - \frac {\text{OCV}} {\text{SCC}} x \end{align}$$

How about inline equations? $2+2=4$ Yeah, that works. With underscores? $x_b=y_a$ And more? $V_{\text{A}} = \big( x \big) _A \cdot j_ A$

Inline accidental html? $x<b>y$ but this should NOT be bold $5</b>3$

What if we have some money involved?

$$\text{Cost} = \$5$$

What if we have some money involved? $\text{Cost} = \$5$ . That should be fine, right? $\$100$ .

How about standalone ones?

$$x+y=z^3$$

And multi-line?

$$ \begin{align} x+y & = z^3 \\ x & = z^3 - y \end{align} $$

What if I leave blank lines?

$$ \begin{align} x+y & = z^3 \\ x & = z^3 - y \end{align} $$

OK, now we’re cooking.


How about a circuit?

Exercise It’s a thing! Click it! Click it now.

What if we Nest these? Will it Still work????

HELLO-TAG-TEST

What about tags in Headings where conventional things work?  


Let’s do serious equation things:

$$ \begin{equation} \begin{bmatrix} 1 & 0 & 0 \\ 1 & -1 & -100 \\ 0 & 1 & -100 \end{bmatrix} \begin{bmatrix} V_X \\ V_Y \\ i_1 \end{bmatrix} = \begin{bmatrix} 12 \\ 0 \\ 0 \end{bmatrix} \end{equation} $$

We could equivalently write this matrix equation even more compactly as an augmented matrix as described in the Systems of Equations section:

$$ \begin{equation} \left[ \begin{array}{ccc|c} 1 & 0 & 0 & 12 \\ 1 & -1 & -100 & 0 \\ 0 & 1 & -100 & 0 \end{array} \right] \ \text{for} \ (V_X, V_Y, i_1) \end{equation} $$

Inline Math! & 5 < 3 > x  

Before $x$ , between $x \rightarrow \infty$ .

In fact, depending on the structure of our equations and for really huge values of $x$ , it might be appropriate (though usually is not!) to take the full limit of $x \rightarrow \infty$ :

For “small” $x$ , by which we really mean $|x| \ll 1$ , a new approximation is needed for our function $y(x) = \frac {1} {1 + x}$ .

But, for values of $x$ close to 1, we can approximate this fraction with a simpler expression that doesn’t have an $x$ in the denominator. Here’s how we can construct the tangent line around the point $x=1$ :