h(x)=ln(x+2)+0.5x2−4x>−2h(x) = \ln(x + 2) + 0.5x^2 - 4 \quad x > -2h(x)=ln(x+2)+0.5x2−4x>−2
Show that h(x)=0h(x) = 0h(x)=0 has a root in the interval [2.2,2.3][2.2, 2.3][2.2,2.3]
Find h′(x)h'(x)h′(x)
Using x0=2.2x_0 = 2.2x0=2.2 as a first approximation, apply the Newton-Raphson procedure to find a second approximation, giving your answer to 3 decimal places.
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (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.
