Given that \(f(x)=\mathrm e^{\cos x}\), find \(f(0)\), \(f'(0)\) and \(f''(0)\). Hence write down the first two non-zero terms in the Maclaurin series for \(f(x)\). Give the coefficients in terms of \(\mathrm e\).[5]
Given that the first two non-zero terms in the Maclaurin series for \(f(x)\) are equal to the first two non-zero terms in the series expansion of \(\frac1{a+bx^2}\), where \(a\) and \(b\) are constants, find \(a\) and \(b\) in terms of \(\mathrm e\).[4]