CAIE Further Paper 2 2020 June — Question 2

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2020
SessionJune
TopicTaylor series
TypeExponential or trigonometric base functions

2 It is given that \(y = 2 ^ { x }\).
  1. By differentiating \(\ln y\) with respect to \(x\), show that \(\frac { \mathrm { dy } } { \mathrm { dx } } = 2 ^ { \mathrm { x } } \ln 2\).
  2. Write down \(\frac { d ^ { 2 } y } { d x ^ { 2 } }\).
  3. Hence find the first three terms in the Maclaurin's series for \(2 ^ { X }\).