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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /info/examples/FirstSteps/mathb.tex |
Initial commit
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-rw-r--r-- | info/examples/FirstSteps/mathb.tex | 24 |
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diff --git a/info/examples/FirstSteps/mathb.tex b/info/examples/FirstSteps/mathb.tex new file mode 100644 index 0000000000..be97c54155 --- /dev/null +++ b/info/examples/FirstSteps/mathb.tex @@ -0,0 +1,24 @@ +% Sample file: mathB.tex +% Typeset with LaTeX format +\documentclass{article} + +\begin{document} +In first-year calculus, we define intervals such as +%$(u, v)$ and $(u, \infty)$. Such an interval is a + $(u, v)$ and (u, \infty)$. Such an interval is a + \emph{neighborhood} of $a$ +if $a$ is in the interval. Students should +realize that $\infty$ is only a +symbol, not a number. This is important since +we soon introduce concepts + such as $\lim_{x \to \infty} f(x)$. +%such as $\lim_{x \to \infty f(x)$. + +When we introduce the derivative, +\[ + \lim_{x \to a} \frac{f(x) - f(a)}{x - a} + %\lim_{x \to a} \frac{f(x) - f(a) x - a} +\] +we assume that the function is defined and continuous +in a neighborhood of $a$. +\end{document} |