In the triangle \(ABC\), \(AB=1\), \(BC=3\) and angle \(ABC=\theta\) radians. Given that \(\theta\) is a sufficiently small angle, show that \(AC\approx(4+3\theta^2)^{1/2}\approx a+b\theta^2\), for constants \(a\) and \(b\) to be determined.[5]
Given that \(f(x)=\tan(2x+\frac14\pi)\), find \(f(0)\), \(f'(0)\) and \(f''(0)\). Hence find the first 3 terms in the Maclaurin series of \(f(x)\).[5]