2020 HCI C1CT2 Q1

1. Without using a calculator, solve the inequality
   \(\frac{x}{1-16{{x}^{4}}}\le \frac{x}{4{{x}^{2}}+1}\).[4]

Hence solve the following inequalities,

2. \(\frac{\left| x \right|}{1-16{{x}^{4}}}\le \frac{\left| x \right|}{4{{x}^{2}}+1}\),[2]
3. \(\frac{\sin x}{1-16{{\left( \sin x \right)}^{4}}}\le \frac{\sin x}{4{{\left( \sin x \right)}^{2}}+1}\) for \(0\le x\le 2\pi \), giving your answers in exact form.[3]