CAIE P2 2009 November — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2009
SessionNovember
TopicParametric equations

4 The parametric equations of a curve are $$x = 1 - \mathrm { e } ^ { - t } , \quad y = \mathrm { e } ^ { t } + \mathrm { e } ^ { - t }$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \mathrm { e } ^ { 2 t } - 1\).
  2. Hence find the exact value of \(t\) at the point on the curve at which the gradient is 2 .