jsewell94
- 23
- 0
Homework Statement
The first three terms of a Taylor Series centered about 1 for ln(x) is given by:
\frac{x^{3}}{3} - \frac{3x^{2}}{2} + 3x - \frac{11}{6}
and that
\int{ln(x)dx} = xlnx - x + c
Show that an approximation of ln(x) is given by:
\frac{x^3}{12} - \frac{x^2}{2} + \frac{3x}{2} - \frac{5}{6} - \frac{1}{4x}
2. The attempt at a solution
I have tried this problem a few times, but it is becoming clear that I am missing some crucial step/idea. Basically, what I have tried is setting lnx equal to the Taylor Series, integrating both sides, and solving for lnx. However, when I do this, I manage to get all of the necessary terms EXCEPT for the 1/4x. Where does that come from, exactly? If someone could help, that'd be awesome! :D
Thanks!