Content deleted Content added
"rate" and "amount" should be equivalent to the non-mathematicians; but mathematicians prefer the former. Highlight that "proportional" is a departure from the (natural) exponential function where it is instead "equal". (Perhaps too subtle?) |
→Power series: People don't say "term-by-term derivation" |
||
Line 66:
&=\sum_{n=0}^\infty \frac{x^n}{n!},\end{align}</math>
[[Image:Exp series.gif|right|thumb|The exponential function (in blue), and the sum of the first {{math|''n'' + 1}} terms of its power series (in red)]]
where <math>n!</math> is the [[factorial]] of {{mvar|n}} (the product of the {{mvar|n}} first positive integers). This series is [[absolutely convergent]] for every <math>x</math> per the [[ratio test]]. So, the derivative of the sum can be computed by term-by-term
===Functional equation===
| |||