f(x)=ln(5x+1)+x2−6x>−0.2f(x) = \ln(5x + 1) + x^2 - 6 \quad x > -0.2f(x)=ln(5x+1)+x2−6x>−0.2
Show that f(x)=0f(x) = 0f(x)=0 has a root in the interval [1.9,2.0][1.9, 2.0][1.9,2.0]
Find f′(x)f'(x)f′(x)
Using x0=1.9x_0 = 1.9x0=1.9 as a first approximation, apply the Newton-Raphson procedure to find a second approximation, giving your answer to 3 decimal places.
329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.