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9231 P11 - Jun 2023 - Q06 - 15 marks
4204

The curve C has equation \(y = \frac{x^2 + 2x - 15}{x - 2}\).

  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 intersections with the axes.
  4. Sketch the curve with equation \(y = \left| \frac{x^2 - 2x - 15}{x - 2} \right|\).
  5. Find the set of values of \(x\) for which \(\left| \frac{2x^2 + 4x - 30}{x - 2} \right| < 15\).
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