CAIE Further Paper 2 2022 June — Question 5

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2022
SessionJune
TopicImplicit equations and differentiation

5 The variables \(x\) and \(y\) are such that \(y = 0\) when \(x = 0\) and $$( x + 1 ) y + ( x + y + 1 ) ^ { 3 } = 1$$
  1. Show that \(\frac { \mathrm { dy } } { \mathrm { dx } } = - \frac { 3 } { 4 }\) when \(x = 0\).
  2. Find the Maclaurin's series for \(y\) up to and including the term in \(x ^ { 2 }\).