Question

Find the Maclaurin Series of the following functions:

(a) f(x)= Ln(3+x)

(b) f(x)= cos(3x)

(c) f(x) = x^(2)(e^(-x))

Answer 1

A Maclaurin series is a Taylor series expansion of a function about 0. A Maclaurin series is used to approximate a function, verify the antiderivative of a complicated function, or compute an otherwise uncomputable sum. As we are familiar with the Maclaurin formula the series is calculated by taking derivatives of a given function at where, x = 0. The five-time derivatives for x=0 are calculated and their values are put in the formula and calculated in the series. Thus, the series is simplified and similarly calculated for the remaining two functions. 

Maclaurin series is used to approximate a function,