by William Elliot <marsh@[EMAIL PROTECTED]
>
Mar 10, 2008 at 03:54 AM
On Mon, 10 Mar 2008 baz90@[EMAIL PROTECTED]
wrote:
> Hello; a simple question if someone could please show how to do it; a
> cube has side length 15cm. What is the max. possible % error in the
> volume? thanks if you can help. baz
>
Let x be the side of the cube and dx a small error in x.
Then V(x) = x^3 and V(x + dx) = x^3 + 3x^2 dx + 3x dx^2 + dx^3.
The dx^2 and dx^3 terms can usually be ignored when dx is small.
For example. x = 1, dx = 1/10 or dx = 1/20.
The usual calculus approximation for error is
V(x + dx) = V'(x) + 3x^2 dx
which if you notice is the same result gotten by ignoring
dx^2 and dx^3 for being too small to be notice.
