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)−31
Hence, 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)−13W(\theta) = \cos(5\theta) + \left(1 - \frac{3}{2}\theta^2\right)^{-\frac{1}{3}}W(θ)=cos(5θ)+(1−23θ2)−31 can be approximated by A+Bθ+Cθ2A + B\theta + C\theta^2A+Bθ+Cθ2, where AAA, BBB and CCC are constants to be found.
Practise Edexcel A Level Maths 4.2 Expanding (a + bx)^n with exam-style questions for A Level Maths. 99 questions, matched to the Edexcel A Level Maths (9MA0) 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.