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.)
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.