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Gods Gift To Calculators: The Taylor Series
Beginning of essay
It is incredible how far calculators have come since my parents were in
college, which was when the 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 gott ....
Middle of essay
....es match the the derivatives of f(x) at
x=0. So if we want to make the derivatives of fn(x) equal to f(x) at x=0, we
have to chose the coefficients a0 through an properly. How do we do this?
We'll write down the polynomial and its derivatives as follows.
fn(x)= a0 + a1x + a2x2 + a3x3 + ... + anxn
f1n(x)= a1 + 2a2x + 3a3x2 +... + nanxn-1
f2n(x)= 2a2 + 6a3x +... +n(n-1)anxn-2
.
.
f(n)n(x)= (n!)an
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| Number of words: 545 |
Approximate pages: 2 |
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