Determine the first two terms, in ascending powers of uuu, of the binomial expansion of
(1+34u)−13 \left(1 + \frac{3}{4}u\right)^{-\frac{1}{3}} (1+43u)−31Hence, in a signal processing application, for small phase offsets θ\thetaθ, show that the windowing function W(θ)W(\theta)W(θ) defined by
W(θ)=cos(5θ)+(1−32θ2)−13 W(\theta) = \cos(5\theta) + \left(1 - \frac{3}{2}\theta^2\right)^{-\frac{1}{3}} W(θ)=cos(5θ)+(1−23θ2)−31can be approximated by A+Bθ+Cθ2A + B\theta + C\theta^2A+Bθ+Cθ2, where AAA, BBB and CCC are constants to be found.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
