A chemical engineer is modeling the yield, YYY, of a reaction as a function of the catalyst concentration, ccc. The relationship is given by the formula:
Y(c)=1+6c23∣c∣<16 Y(c) = \sqrt[3]{1 + 6c^2} \quad \quad |c| < \frac{1}{\sqrt{6}} Y(c)=31+6c2∣c∣<61Find, in ascending powers of ccc, the first three non-zero terms of the binomial series expansion of Y(c)Y(c)Y(c), giving each coefficient as a simplified fraction.
Use the expansion from part (a) with c=13c = \frac{1}{3}c=31 to find a rational approximation to k⋅53k \cdot \sqrt[3]{5}k⋅35, where kkk is a constant you must determine.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
