Questions — WJEC Further Unit 4 (51 questions)

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WJEC Further Unit 4 Specimen Q12
12. The function \(f\) is given by $$f ( x ) = \mathrm { e } ^ { x } \cos x$$
  1. Show that \(f ^ { \prime \prime } ( x ) = - 2 \mathrm { e } ^ { x } \sin x\).
  2. Determine the Maclaurin series for \(f ( x )\) as far as the \(x ^ { 4 }\) term.
  3. Hence, by differentiating your series, determine the Maclaurin series for \(\mathrm { e } ^ { x } \sin x\) as far as the \(x ^ { 3 }\) term.
  4. The equation $$10 \mathrm { e } ^ { x } \sin x - 11 x = 0$$ has a small positive root. Determine its approximate value, giving your answer correct to three decimal places.