maclaurin series: (e^x)*sin(x), {ln(1 + x)}/(1 - x)

[johnq2k7]

Find the first four terms of the Maclaurin series for each of the functions given below:

a.) (e^x)*sin(x)

b.) {ln (1+x)}/(1-x)

for shown:

e^x= 1+x+(x^2)/2! +(x^3)/3!+.... for all x

sin(x)= x- (x^3)/3!+ (x^5)/5! - (x^7)/7!

1/1-x is a geometric series of sigma n=0 to inf. of x^n for |x|<1

i need some serious help here

 

[BigGlenntheHeavy]

Re: maclaurin series serious help needed!

\(\displaystyle e^{x}sin(x)= x+x^{2}+x^{3}/3\)
\(\displaystyle Ln(1+x)/(1-x) = x+x^{2}/2+5x^{3}/6+7x^{4}/12\)