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1.7.1 Binomial expansion

Determine the first two terms, in ascending powers of $u$ , of the binomial expansion of

\left(1 + \frac{3}{4}u\right)^{-\frac{1}{3}}

[2]

Hence, in a signal processing application, for small phase offsets $θ\theta$ , show that the windowing function $W(θ)W(\theta)$ defined by

W(\theta) = \cos(5\theta) + \left(1 - \frac{3}{2}\theta^2\right)^{-\frac{1}{3}}

can be approximated by $B\theta + C\theta^2$ , where $A$ , $B$ and $C$ are constants to be found.

[4]

1.7.1 Binomial expansion Questions

144 exam-style questions on AQA A Level Maths 1.7.1 Binomial expansion. Each one has a worked solution and a mark scheme showing where the marks go.

Determine the first two terms, in ascending powers of $u$ , of the binomial expansion of

\left(1 + \frac{3}{4}u\right)^{-\frac{1}{3}}

[2]

Hence, in a signal processing application, for small phase offsets $θ\theta$ , show that the windowing function $W(θ)W(\theta)$ defined by

W(\theta) = \cos(5\theta) + \left(1 - \frac{3}{2}\theta^2\right)^{-\frac{1}{3}}

can be approximated by $B\theta + C\theta^2$ , where $A$ , $B$ and $C$ are constants to be found.

[4]

144 exam-style questions on AQA A Level Maths 1.7.1 Binomial expansion. Each one has a worked solution and a mark scheme showing where the marks go.