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.
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.