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)−31A 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)−31Hence, 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+Cx2where AAA, B B\,B and C C\,C are constants to be found.