(a) A curve has equation \(y=\mathrm{e}^{x}+\frac{1}{4} \mathrm{e}^{-x}\), for \(0 \leqslant x \leqslant 1\). Find, in terms of \(\pi\) and e , the area of the surface generated when the curve is rotated through \(2 \pi\) radians about the \(x\)-axis.
(b) Using standard results from the list of formulae (MF19), or otherwise, find the Maclaurin's series for \(\mathrm{e}^{x}+\frac{1}{4} \mathrm{e}^{-x}\) up to and including the term in \(x^{2}\).