A curve has the equation
y=ln(3−2x)+x2−2xy = \ln(3 - 2x) + x^2 - 2xy=ln(3−2x)+x2−2x
The curve intersects the xxx-axis at exactly one point.
Show that the xxx-coordinate of this point lies between 0 and 1.
Use the Newton-Raphson method, with x0=1x_0 = 1x0=1, to find the xxx-coordinate of this point, giving your answer correct to five decimal places. Show the result of each iteration.
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.