Tag: Equations
Differentials and Linear Approximation
by theorangedog on Jan.11, 2008, under Skills
Q. Find the linear change in volume dV if the sides of a cube change from 10 to 10.1.
A. We can use the definition of 
to determine the estimated linear change. In this problem, we start with the cubic volume equation of 
where 
is the length of one side of the cube. The derivative is then 
. Filling in for linear approximation we get 
. This results in 
. We can see that the linear approximation is not entirely accurate, hence the name approximation, as 
.
Related equations and relationships:
If 
then 
is increasing. If 
then is decreasing.
LaTeX Test
by theorangedog on Nov.02, 2007, under Skills
![R(t,s) = frac{E[(X_{t} - mu)(X_{s} - mu)]}{sigma^2}](http://theorangedog.net/wp-content/cache/tex_990d1254eb7eef7b58c8a2484981d109.gif)
I’m using mimeTex as a substitute for LaTeX due to its ease of installation and use. Just to make sure it works, above is the equation for the autocorrelation function.
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