Prerequisite – Taylor theorem and Taylor series
We know that formula for expansion of Taylor series is written as:
Now if we put a=0 in this formula we will get the formula for expansion of Maclaurin series. T
hus Maclaurin series expansion can be given by the formula –
Maclaurin series expansion of some elementary functions :
- Exponential function :
Differentiating n times,
So we get
- f(x) = cos x
- f(x) = sin x
- f(x) = (ax + b)^m
- f(x) = ln(1+x)
- f(x) = ln(1-x)
Find the first seven terms of f(x) = ln(sec x).
Differentiating w.r.t. x,
Thus we get the Maclaurin series as –
Evaluate Maclaurin series for tan x.
Thus we get Maclaurin series as –
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