Quelpr
10 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2023 · Paper 2 · Question 3(c)

Use mathematical induction to prove that dⁿ/dxⁿ (eˣ sin x) = 2ⁿ/² eˣ sin(x + nπ/4). You may use the fact that sin x + cos x = √2 sin(x + π/4) and that dᵏ⁺¹/dxᵏ⁺¹ f(x) = d/dx (dᵏ/dxᵏ f(x)).

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 3(a)Determine the coefficient of x⁴ in the binomial expansion of (1 - 2x) / (1 + 3x)².[7 marks]
  2. 3(b)Show that if the series 1 + (7 / (3x - 5)) + (7 / (3x - 5))² + (7 / (3x - 5))³ + ... converges, then its sum to infinity is (3x - 8) / (3x - 12).[8 marks]

More practice: the rest of this paper · more Differentiation II questions · all CAPE Pure Mathematics Unit 2 past papers