The natural logarithm function is defined for by g(x)= ! (1+3x^ 2 )
MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
The natural logarithm function g is defined for ∣x∣<31 by
g(x)=ln(1+3x2).
Answer the following.
(a) Derive the first four non-zero terms of the power-series representation of g centered at x=0 and write a general term for the series.
(b) State the radius of convergence of the series from part (a) and justify your answer.
(c) Use the series to approximate g(0.2) so that the magnitude of the error does not exceed 10−5. Justify that your approximation meets the required accuracy.