1. ## Lagrange Error

Estimate ln(1.3) using a third degree Taylor polynomial about a=0 and find the error bound.

2. Originally Posted by seebs15
Estimate ln(1.3) using a third degree Taylor polynomial about a=0 and find the error bound.
note the series is alternating, so an error bound can be determined by the first omitted term of the Taylor polynomial.

$\ln(1+x) \approx P_3(x) = x - \frac{x^2}{2} + \frac{x^3}{3}$

$\ln(1.3) \approx P_3(0.3) = 0.3 - \frac{0.3^2}{2} + \frac{0.3^3}{3} = 0.264$

$|\ln(1.3) - P_3(0.3)| < \left|-\frac{0.3^4}{4}\right| = .0020250...$