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 (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.