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
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)−13G(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+Cx2G(x) \approx A + Bx + Cx^2G(x)≈A+Bx+Cx2 where AAA, B B\,B and C C\,C 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.