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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).
if a,b,c are in HP
determine the equation that represent the following lines be sure to define your variable and show all of your work
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