Gods Gift To Calculators: The Taylor Series
Beginning of paper
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 paper
.... out. First, lets assume that we have a function in the form
y= f(x) that looks like the graph below.
We'll start out trying to approximate function values near x=0. To do
this we start out using the lowest order polynomial, f0(x)=a0, that passes
through the y-intercept of the graph (0,f(0)). So f(0)=ao.
Next, 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 approximat ....
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Word count: 545
Page count: 2 (approximately 250 words per page)
