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

1. Find the equations of the asymptotes of C.
2. Show that C has no stationary points.
3. Sketch C, stating the coordinates of the point of intersection with the y-axis and labelling the asymptotes.
4. 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 \(a\).