The curve \(C\) has equation \(y = \frac{x^2 + ax + 1}{x + 2}\), where \(a > \frac{5}{2}\).

1. (a) Find the equations of the asymptotes of \(C\).
2. (b) Show that \(C\) has no stationary points.
3. (c) Sketch \(C\), stating the coordinates of the point of intersection with the \(y\)-axis and labelling the asymptotes.
4. (d)
   1. Sketch the curve with equation \(y = \left| \frac{x^2 + ax + 1}{x + 2} \right|\).
   2. On your sketch in part (i), draw the line \(y = a\).
   3. It is given that \(\left| \frac{x^2 + ax + 1}{x + 2} \right| < a\) for \(-5 - \sqrt{14} < x < -3\) and \(-5 + \sqrt{14} < x < 3\). Find the value of \(a\).