Binomial Expansion

Question 2

In a high-frequency signal filter design, the gain $G$ relative to a frequency shift $ω\omega$ is modelled by the function $G(ω)=(25+2ω)−12G(\omega) = (25 + 2\omega)^{-\frac{1}{2}}$ . The first three terms, in ascending powers of $ω\omega$ , of the binomial expansion of $G(ω)G(\omega)$ are given by

2\omega)^{-\frac{1}{2}} \approx a - \frac{1}{125}\omega + \frac{3}{6250}\omega^2

where $a$ is a constant.

a.

State the range of values of $ω\omega$ 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

[1]

b.

Find the value of $a$ .

Choose from the options below:

12515525\frac{1}{25} \quad \frac{1}{5} \quad 5 \quad 25

[1]

Binomial Expansion

1 2 3 4

Question 2

In a high-frequency signal filter design, the gain $G$ relative to a frequency shift $ω\omega$ is modelled by the function $G(ω)=(25+2ω)−12G(\omega) = (25 + 2\omega)^{-\frac{1}{2}}$ . The first three terms, in ascending powers of $ω\omega$ , of the binomial expansion of $G(ω)G(\omega)$ are given by

2\omega)^{-\frac{1}{2}} \approx a - \frac{1}{125}\omega + \frac{3}{6250}\omega^2

where $a$ is a constant.

a.

State the range of values of $ω\omega$ 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

[1]

b.

Find the value of $a$ .

Choose from the options below:

12515525\frac{1}{25} \quad \frac{1}{5} \quad 5 \quad 25

[1]

Binomial Expansion

Question 2

Binomial Expansion Questions

Binomial Expansion

Question 2

Binomial Expansion Questions