f(x)=sin(2x)+ln(x)x>0f(x) = \sin(2x) + \ln(x) \quad x > 0f(x)=sin(2x)+ln(x)x>0
Given that f′(x)=2cos2x+1x\displaystyle f'(x) = 2 \cos 2x + \frac{1}{x}f′(x)=2cos2x+x1, show that y=f(x)y = f(x)y=f(x) has a stationary point in the interval [1,1.1][1, 1.1][1,1.1]
The x x\,x coordinate of the stationary point is approximately 1.037. Starting with x0=1.05x_0 = 1.05x0=1.05, apply the Newton-Raphson procedure twice to verify this approximation.
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.