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Example: Determine the Taylor series for f(x) = ex about x=0.
Solution
It is probably one of the easiest functions to get the Taylor series for. We just require recalling that,
f(n)(x) = ex n = 0,1,2,.....
Therefore we find,
f(n)(0) = 1 n = 0,1,2,.....
The Taylor series for this illustration is then,
Obviously, it's frequently easier to find the Taylor series about x=0 but we don't all the time do that.
Definition
A function, f(x), is termed as analytic at x=a if the Taylor series for f(x) regarding to x=a has a positive radius of convergence and converges to f(x).
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is 1/6 same as six times less
1+2+3+.....+n=1/2n(n+1)
Example Suppose the demand and cost functions are given by Q = 21 - 0.1P and C = 200 + 10Q Where, Q - Quantity sold
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