Find out the taylor series for f (x) = ex about x = 0, Mathematics

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Find out the Taylor Series for f (x) = ex 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) = ex                             n = 0,1,2,3,....

and so

f(n) (0) = e0 = 1                       n = 0,1,2,3,...

Hence, the taylor series for f (x) = ex about x=0 is,

1870_Find out the Taylor Series for f (x) = ex about x = 0.png


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