% EXERCISE SIX
          
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	\textbf{Exercise Six: Sizing and Spacing}
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A geometric progression: 1\hspace{1cm}2\hspace{2cm}4\hspace{4cm}8

\hspace{1cm}[\verb!Each space in the above should be double the previous.!]\\

Suppose $y=\sqrt[3]{x}$. Then, the derivative of $y$ with respect to $x$
 at $x=64$ is written in Leibniz notation as

$$\frac{dy}{dx}\biggr|_{x=64}=\frac{1}{3x^{2/3}}\biggr|_{x=64}=\frac{1}{48}$$\\

A set that's bounded below but has no smallest element is 
$$\left\{1, \frac{1}{2},\frac{1}{3}, \frac{1}{4}, \dots\right\}=
\left\{\frac{1}{n} \biggm| n\in\mathbb{N}\right\}$$

Did you know that 
$\displaystyle\lim_{n\to\infty}\left(1+\frac{1}{26n}\right)^{13n} = \sqrt{e}$? 
Well, it does.

Some colleges we know are \Tiny Colby, \Small Bowdoin, and \Huge Bates. 
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