2022 SJI P2 Q2

2022 SJI P2 Q2

IB Year 5 | Grade 11
9 marks
  1. Obtain the series expansion of \(\sqrt{3+4x}\), up to and including the term in \(x^2\).[4]
  2. Explain why it is not suitable to use \(x=1\) to give an approximation for \(\sqrt7\).[2]
  3. Use \(x=-\dfrac16\) to find an approximation for \(\sqrt7\), giving your answer correct to \(3\) decimal places.[3]

Solution:

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Answer:(a) \(\sqrt3\left(1+\dfrac23x-\dfrac29x^2+\cdots\right)\) (b) Outside \(|x|<\dfrac34\) (c) \(2.648\)

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