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.)