A hydraulic system's pressure efficiency, E(h)E(h)E(h), at a depth hhh meters is modeled by the function
E(h)=(14−10h)12∣h∣<0.025 E(h) = \left(\frac{1}{4} - 10h\right)^{\frac{1}{2}} \quad |h| < 0.025 E(h)=(41−10h)21∣h∣<0.025Find the first 4 terms, in ascending powers of hhh, of the binomial expansion of E(h)E(h)E(h), giving each coefficient in its simplest form.
By substituting h=0.01h = 0.01h=0.01 into your expansion from part (a), find an approximation for 15\sqrt{15}15.
Give your answer in the form ab\frac{a}{b}ba where aaa and bbb are integers to be found.
144 exam-style questions on AQA A Level Maths 1.7.1 Binomial expansion. Each one has a worked solution and a mark scheme showing where the marks go.