In a high-frequency signal filter design, the gain GGG relative to a frequency shift ω\omegaω is modelled by the function G(ω)=(25+2ω)−12G(\omega) = (25 + 2\omega)^{-\frac{1}{2}}G(ω)=(25+2ω)−21. The first three terms, in ascending powers of ω\omegaω, of the binomial expansion of G(ω)G(\omega)G(ω) are given by (25+2ω)−12≈a−1125ω+36250ω2(25 + 2\omega)^{-\frac{1}{2}} \approx a - \frac{1}{125}\omega + \frac{3}{6250}\omega^2(25+2ω)−21≈a−1251ω+62503ω2 where aaa is a constant.
State the range of values of ω\omegaω for which this expansion is valid.
Choose from the options below: ∣ω∣<225∣ω∣<252∣ω∣<5∣ω∣<25|\omega| < \frac{2}{25} \quad |\omega| < \frac{25}{2} \quad |\omega| < 5 \quad |\omega| < 25∣ω∣<252∣ω∣<225∣ω∣<5∣ω∣<25
Find the value of aaa.
Choose from the options below: 12515525\frac{1}{25} \quad \frac{1}{5} \quad 5 \quad 2525151525
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 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.