Question

Use the Taylor series for ln(1−x) to find the Taylor series for xln(1+4x).

Answer 1

To find the Taylor series for xln(1+4x), substitute -x with 4x in the Taylor series expansion for ln(1-x).

Step-by-step explanation:

To find the Taylor series for xln(1+4x), we can start with the Taylor series for ln(1-x). The Taylor series expansion for ln(1-x) is given by:

-x - (x^2)/2 - (x^3)/3 - ...

Now, to find the Taylor series for xln(1+4x), we can substitute -x with 4x in the above series:

-4x - (4x^2)/2 - (4x^3)/3 - ...

This is the Taylor series for xln(1+4x).