CAIE P2 2024 November — Question 6

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2024
SessionNovember
TopicParametric equations

6 A curve has parametric equations $$x = \frac { \mathrm { e } ^ { 2 t } - 2 } { \mathrm { e } ^ { 2 t } + 1 } , \quad y = \mathrm { e } ^ { 3 t } + 1$$
  1. Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
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    \includegraphics[max width=\textwidth, alt={}, center]{dcc483e9-630e-4f02-ad8c-4a27c0720fc6-11_2725_35_99_20}
  2. Find the exact gradient of the curve at the point where the curve crosses the \(y\)-axis.