The sensitivity $S\,$ of a precision transducer depends on the frequency $\omega\,$ of pressure oscillations according to the model

S(\omega) = (1 + k\omega)^{-\frac{1}{2}}, \quad |k\omega| < 1

where $k\,$ is a constant. Given that the binomial expansion of $S(ω)S(\omega)$ in ascending powers of $\omega\,$ up to the term in $\omega^3\,$ is

0.6\omega + P\omega^2 + Q\omega^3

(i) find the value of $k$ ,

(ii) find the value of the constant $P\,$ and the constant $Q$ .

Use the expansion to find an approximate value to $10.88\displaystyle \frac{1}{\sqrt{0.88}}$ .

Show your working and give your answer to 6 decimal places.

The sensitivity $S\,$ of a precision transducer depends on the frequency $\omega\,$ of pressure oscillations according to the model

S(\omega) = (1 + k\omega)^{-\frac{1}{2}}, \quad |k\omega| < 1

where $k\,$ is a constant. Given that the binomial expansion of $S(ω)S(\omega)$ in ascending powers of $\omega\,$ up to the term in $\omega^3\,$ is

0.6\omega + P\omega^2 + Q\omega^3

(i) find the value of $k$ ,

(ii) find the value of the constant $P\,$ and the constant $Q$ .

Use the expansion to find an approximate value to $10.88\displaystyle \frac{1}{\sqrt{0.88}}$ .

Show your working and give your answer to 6 decimal places.

3.3 Sequences and series (A-level only)

3.3 Sequences and series (A-level only) Questions