It is given that
f(x)=sin2x+lnxf(x) = \sin 2x + \ln xf(x)=sin2x+lnx, x>0 x > 0\,x>0
where x x\,x is measured in radians.
Show that the curve 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].
Starting with x0=1.05x_0 = 1.05x0=1.05, apply the Newton-Raphson procedure twice to find an approximation for the xxx-coordinate of this stationary point. Give your answers to four decimal places.
125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.