Pg 12 Q1 – 2015 MI Q3

(i)

Expand \(\frac{\sqrt[4]{1+3{{x}^{2}}}}{2+x}\) in ascending powers of \(x\), up to and including the term in \({{x}^{2}}\).

[3]

(ii)

Find the set of values of \(x\) for which the expansion in part (i) is valid.

[2]

(iii)

By substituting \(x=-\frac{1}{4}\) and using your result in part (i), show that \(\sqrt[4]{19}\approx \frac{p}{q}\), where \(p\) and \(q\) are integers to be determined.

[2]