CAIE P3 2021 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionJune
TopicParametric equations

6 The parametric equations of a curve are $$x = \ln ( 2 + 3 t ) , \quad y = \frac { t } { 2 + 3 t }$$
  1. Show that the gradient of the curve is always positive.
  2. Find the equation of the tangent to the curve at the point where it intersects the \(y\)-axis.