Exploring Taylor Series for f(x) and g(x)

[morbello]

ive got a question to ask I am working on taylor series and want to know

f(x)=In(3+x) and g(x)=In (1+x)

by writing

In(3+x)=In3+In(1+1/3x)
im asked to use substitution in one off the standard taylor series given in the course.to find about 0 for f

explicitly all terms up to term in x^3

im not sure were to start.

I have

x+1/3 x^2+1*2/3 x^3+1*2*3/3 x^4+...

 

[fluidistic]

I think you forgot to provide the function you're trying to find its Taylor's polynomial.

 

[gc2285]

the function is ln(3+x) but you are told to write it as ln3 + ln(1 + x/3)

I believe you just need the standard series of ln (1+x) but sub in x/3 for the x.

So you would end up with

ln3 + x/3 - (x^2)/18 + (x^3)/81