How do you obtain the Maclaurin series for #f(x)= x^2ln(1+x^3)#?
1 Answer
Mar 11, 2015
Hi,
-
First, you have to know the usual serie :
#ln(1+X) = X - X^2/2 + X^3/3 + \ldots + (-1)^(n-1)X^n/n + o_{X->0}(X^n)# -
Second, you can take
#X=x^3# because if#x->0# , then#x^3->0# . So,
#ln(1+x^3) = x^3 - x^6/2 + x^9/3+\ldots + (-1)^(n-1)x^{3n}/n + o_{x->0}(x^(3n))# -
Finally, multiply by
#2x# :
#2x ln(1+x^3) = 2x^4 - x^7 + 2/3 x^10+ \ldots + (-1)^(n-1)2/n x^{3n+1} + o_{x->0}(x^(3n+1))#
