The sensitivity S(x)S(x)S(x) of a precision electronic sensor is modeled by the function S(x)=(1+4x)−12S(x) = (1 + 4x)^{-\frac{1}{2}}S(x)=(1+4x)−21, where xxx is a small dimensionless parameter.
Find the first three terms, in ascending powers of xxx, of the binomial expansion of S(x)S(x)S(x).
An engineer attempts to use this expansion with x=0.3x = 0.3x=0.3 to calibrate the sensor. Explain why this approach is invalid.
By substituting x=−0.05x = -0.05x=−0.05 into your expansion, find an approximation for 5\sqrt{5}5. Give your answer to three significant figures.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
