- Solve \(2 \sin x = \tan x\) exactly, where \(- \frac { \pi } { 2 } < x < \frac { \pi } { 2 }\).
- Let \(a , b\) satisfy \(0 < a < b\).
i. Find, in terms of \(a\) and \(b\), the value of
$$\int _ { a } ^ { b } \frac { 81 } { x ^ { 4 } } d x$$
ii. Explaining clearly any limiting processes used, find the value of \(a\), given that
$$\int _ { a } ^ { \infty } \frac { 81 } { x ^ { 4 } } d x = \frac { 216 } { 125 }$$