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Gods Gift To Calculators: The Taylor Series
Part 1 of Paper
....e square root key came out. Calculators since then
have evolved into machines that can take natural logarithms, sines, cosines,
arcsines, and so on. The funny thing is that calculators have not gotten any
"smarter" since then. In fact, calculators are still basically limited to the
four basic operations: addition, .... Part 2 of Paper
....t, we see that the graph of f1(x)= a0 + a1x will also pass through x=
0, and will have the same slope as f(x) if we let a0=f1(0).
Now, if we want to get a better polynomial approximation for this
function, which we do of course, we must make a few generalizations. First, we
let the polynomial fn(x)= a0 + a1x + a2x2 + ... + anxn approximate f(x) near x=0,
and let this functions first n derivatives match the the derivatives of f(x) at
x=0. So if we want to make the derivatives of fn(x) equal to.... |
| Number of words: 545 - Approximate pages: 2 |
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