1.3 Sequences and series

a.

Find the first two terms, in ascending powers of $u$ , of the binomial expansion of

2u)^{\frac{1}{3}}

[2]

b.

Hence, for small values of $x$ , show that

\cos 3x + \sqrt[3]{1 - x^2} \approx A + Bx + Cx^2

where $A$ , $B$ and $C$ are constants to be found.

[5]

a.

Find the first two terms, in ascending powers of $u$ , of the binomial expansion of

2u)^{\frac{1}{3}}

[2]

b.

Hence, for small values of $x$ , show that

\cos 3x + \sqrt[3]{1 - x^2} \approx A + Bx + Cx^2

where $A$ , $B$ and $C$ are constants to be found.

[5]

1.3 Sequences and series Questions