Problems DB: The Sandbox

Try Editing This Page
Some LaTeX You Can Play With
1. A Problem!
2. A Bonus Problem

Try Editing This Page

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Save your edits and (if you wrote valid latex) admire how everything is updated.
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Some LaTeX You Can Play With

Here is a problem!

A Problem!

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

• pdf
• pdf tight
• latex

Tags: practice, editors

A Bonus Problem

$When a model rocket is launched, the propellant burns for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for awhile and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts down. The parachute slows the rocket to keep it from breaking when it lands. The figure below shows velocity data from the flight of a model rocket. Use the data to answer the questions below. \begin{enumerate} \item How fast was the rocket climbing when the engine stopped? \item For how many seconds did the engine burn? \item When did the rocket reach its highest point? What was its velocity there? \item When did the parachute pop out? How fast was the rocket falling then? \item How long did the rocket fall before the parachute opened? \item Very carefully sketch a graph of the height of the rocket (in feet) versus time (in seconds). \begin{center} \includegraphics[width=2.3in]{../rocket.pdf} \end{center} \end{enumerate}$

• pdf
• pdf tight
• latex and fig 1

This problem looks better in PDF (try the link). The original figure, sadly, is a little blurry.

Tags: practice, editors

The Sandbox

Contents

Try Editing This Page

Some LaTeX You Can Play With

A Problem!

A Bonus Problem