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.
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.