Use the Maclaurin series for \(\ln ( 1 + x )\) up to the term in \(x ^ { 3 }\) to obtain an approximation to \(\ln 1.5\).
(A) Find the error in the approximation in part (i).
(B) Explain why the Maclaurin series in part (i), with \(x = 2\), should not be used to find an approximation to \(\ln 3\).
Find a cubic approximation to \(\ln \left( \frac { 1 + x } { 1 - x } \right)\).
(A) Use the approximation in part (iii) to find approximations to
ln 1.5 and
\(\quad \ln 3\).
(B) Comment on your answers to part (iv) (A).