f(x)=sin(3x)+ln(x)x>0f(x) = \sin(3x) + \ln(x) \quad x > 0f(x)=sin(3x)+ln(x)x>0
Show that y=f(x)y = f(x)y=f(x) has a stationary point in the interval [0.6,0.7][0.6, 0.7][0.6,0.7]
Starting with x0=0.65x_0 = 0.65x0=0.65, apply the Newton-Raphson procedure twice to find an approximation for the x x\,x coordinate of the stationary point in the interval [0.6,0.7][0.6, 0.7][0.6,0.7], giving your answer to 3 significant figures.
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.