Use the binomial expansion to expand
(16+2v)−12∣v∣<8(16 + 2v)^{-\frac{1}{2}} \quad |v| < 8(16+2v)−21∣v∣<8
in ascending powers of vvv, up to and including the term in v2v^2v2, giving each coefficient as a fully simplified fraction.
The pressure PPP in a pneumatic cylinder is modeled by the function
P(v)=12+kv16+2vwhere k is a constant and ∣v∣<8P(v) = \frac{12 + kv}{\sqrt{16 + 2v}} \quad \text{where } k \text{ is a constant and } |v| < 8P(v)=16+2v12+kvwhere k is a constant and ∣v∣<8
Given that the series expansion of P(v)P(v)P(v), in ascending powers of vvv, is
3+916v+qv2+…where q is a constant3 + \frac{9}{16}v + qv^2 + \dots \quad \text{where } q \text{ is a constant}3+169v+qv2+…where q is a constant
find the value of kkk,
find the value of qqq.
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.