Question 0821

Maclaurin Series
2021 Paper 1 Question 7 Variant

Question

It is given that y=e3tan1x,{y=\mathrm{e}^{3 \tan^{-1} x},} for xR.{x \in \mathbb{R}.}
(a)
Show that
(1+x2)d2ydx2=(32x)dydx.(1+x^2)\frac{\mathrm{d}^2y}{\mathrm{d}x^2}=(3-2x)\frac{\mathrm{d}y}{\mathrm{d}x}.
[4]
(b)
Find the first 4 terms of the Maclaurin expansion of e3tan1x.{\mathrm{e}^{3 \tan^{-1} x}.}
[5]

Answer