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Binomial Expansion

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Question 105
a.

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+43​u)−31​
[2]
b.

A signal processing engineer models the gain G G\,G of a circuit at frequency offset x x\,x using the formula:

G(x)=cos⁡(5x)+(1+6x2)−13 G(x) = \cos(5x) + \left(1 + 6x^2\right)^{-\frac{1}{3}} G(x)=cos(5x)+(1+6x2)−31​

Hence, for small values of xxx, show that the gain can be approximated by

G(x)≈A+Bx+Cx2 G(x) \approx A + Bx + Cx^2 G(x)≈A+Bx+Cx2

where AAA, B B\,B and C C\,C are constants to be found.

[4]

Binomial Expansion Questions

  1. A Level
  2. /Maths
  3. /Binomial Expansion

Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 115 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, 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.

Question bank