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Find out the Taylor Series for f (x) = e^{x }about x = 0.
Solution
In fact this is one of the easier Taylor Series that we'll be asked to calculate. To find out the Taylor Series for a function we will need to find out a general formula for f^{(n)}(a). This is one of the some functions in which this is simple to do right from the start.
To obtain a formula for f^{(n)}(0) all we should require to do is recognize that,
f(n) (x) = e^{x} n = 0,1,2,3,....
and so
f(n) (0) = e^{0} = 1 n = 0,1,2,3,...
Hence, the taylor series for f (x) = e^{x} about x=0 is,
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