Find and simplify the first five terms in the Maclaurin series for \(\mathrm { e } ^ { 2 x }\)
6
Hence, or otherwise, write down the first five terms in the Maclaurin series for \(\mathrm { e } ^ { - 2 x }\)
6
Hence, or otherwise, show that the Maclaurin series for \(\cosh ( 2 x )\) is
$$a + b x ^ { 2 } + c x ^ { 4 } + \ldots$$
where \(a\), \(b\) and \(c\) are rational numbers to be determined.