Standard +0.3 This is a straightforward application of standard Maclaurin series technique for Further Maths students. Part (a) requires routine differentiation of ln(1+5x) three times using the chain rule, and part (b) applies the standard Maclaurin formula with derivatives evaluated at x=0. While it's a Further Maths topic, it follows a completely standard procedure with no problem-solving or insight required, making it slightly easier than average overall.
3. (a) Given that \(y = \ln ( 1 + 5 x ) , | x | < 0.2\), find \(\frac { \mathrm { d } ^ { 3 } y } { \mathrm {~d} x ^ { 3 } }\).
(b) Hence obtain the M aclaurin series for \(\ln ( 1 + 5 x ) , | x | < 0.2\), up to and including the term in \(x ^ { 3 }\).
3. (a) Given that $y = \ln ( 1 + 5 x ) , | x | < 0.2$, find $\frac { \mathrm { d } ^ { 3 } y } { \mathrm {~d} x ^ { 3 } }$.\\
(b) Hence obtain the M aclaurin series for $\ln ( 1 + 5 x ) , | x | < 0.2$, up to and including the term in $x ^ { 3 }$.\\
\hfill \mbox{\textit{Edexcel FP2 Q3 [7]}}