Maclaurin series

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 :

1. Exponential function : Differentiating n times, So we get Thus
2. f(x) = cos x …..
3. f(x) = sin x
4. f(x) = (ax + b)^m
5. f(x) = ln(1+x)
6. f(x) = ln(1-x)

Example-1: Find the first seven terms of f(x) = ln(sec x). Explanation : Differentiating w.r.t. x, Thus we get the Maclaurin series as – Example-2: Evaluate Maclaurin series for tan x. Explanation : Thus we get Maclaurin series as –