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# The Sandbox

## Contents

• Try editing the text in the next section.
• Notice the pretty WYSIWYG editor. If you don’t have javascript on, turn it on.
• Try the buttonbar. Hover for a second to see a tooltip.
• Try using key shortcuts for cut/paste/select all/bold/italic/underline.
• You can also have it take over the whole browser window if you want more space. Click that button again to undo.
• Notice the Preview button below the editor window. Use it liberally.
• Notice the Save button below the editor window.
• Save your edits and (if you wrote valid latex) admire how everything is updated.
• Notice the pop-up formatting help (above Username)
• If you truly mess up the page, you can go to “See Past Edits” and rollback to a previous version (perhaps the one before you started editing!).
• You can save a draft (Save Draft). If you leave the editing window, you will see a small Recover Draft link at the bottom of the page.
• You can create a new page by making a link on an existing page.
• Enter the text [[Name_Of_Your_Page?]]. When you save the page, that text will look like [[Name_Of_Your_Page?]]. Notice the question-mark. You can then click on the question-mark to go to an editing page. (Please don’t make a new page there with that name so we can preserve the nice little question mark!)

## Some LaTeX You Can Play With

Here is a problem!

### A Problem!

Find the following limits. Be sure to explain your reasoning at each step. \begin{alignat*}{3} &a)    \lim_{x \to \infty}\frac{x+\sin x }{ 5x+6} &              &b)    \lim_ {x \to \infty}\frac{\sin x }{ x} &              &c)    \lim_{x \to \infty}x \sin \frac{ 1 }{ x} \\ &d)    \lim_{x \to \infty}\frac{x \sin x }{ x^2+5} &              &e) \lim_{x \to \infty}{\sqrt {x^2+x} - x} &              &f) \lim_{x \to \infty}\frac{x^2( 1+ \sin^2x) }{ (x+\sin x )^2} \end{alignat*}

Tags: practice, editors

### A Bonus Problem

When a model rocket is launched, the propellant burns for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for awhile and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts down. The parachute slows the rocket to keep it from breaking when it lands. The figure below shows velocity data from the flight of a model rocket. Use the data to answer the questions below.
1. How fast was the rocket climbing when the engine stopped?
2. For how many seconds did the engine burn?
3. When did the rocket reach its highest point? What was its velocity there?
4. When did the parachute pop out? How fast was the rocket falling then?
5. How long did the rocket fall before the parachute opened?
6. Very carefully sketch a graph of the height of the rocket (in feet) versus time (in seconds).