Question 0821

Maclaurin Series
2021 Paper 1 Question 7 Variant

Question

It is given that y=e2tanx,{y=\mathrm{e}^{2 \tan x},} for xR.{x \in \mathbb{R}.}
(a)
Show that
d2ydx2=y1(dydx)2+lnydydx.\frac{\mathrm{d}^2y}{\mathrm{d}x^2}=y^{-1}\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^2 +\ln y \frac{\mathrm{d}y}{\mathrm{d}x}.
[4]
(b)
Find the first 4 terms of the Maclaurin expansion of e2tanx.{\mathrm{e}^{2 \tan x}.}
[5]

Answer