The efficiency of a prototype thermal engine is modeled by the function E(h)=(5−2h)6E(h) = (5 - 2h)^6E(h)=(5−2h)6, where h h\,h represents a heat-loss coefficient.
Find the first 4 terms, in ascending powers of hhh, of the binomial expansion of (5−2h)6(5 - 2h)^6(5−2h)6, giving each term in its simplest form.
To determine the engine's performance under specific lab conditions, a researcher needs to estimate 4.9464.94^64.946. State the value of h h\,h that should be used in the expansion from part (a) to achieve this. (There is no need to carry out this calculation.)
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.
