f(x)=ln(2x+1)+x2−5x>−0.5,f′(x)=22x+1+2x\displaystyle f(x) = \ln(2x + 1) + x^2 - 5 \quad x > -0.5,\qquad f'(x)=\frac{2}{2x+1}+2xf(x)=ln(2x+1)+x2−5x>−0.5,f′(x)=2x+12+2x
Show that f(x)=0f(x) = 0f(x)=0 has a root in the interval [1.8,1.9][1.8, 1.9][1.8,1.9]
Using x0=1.8x_0 = 1.8x0=1.8 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.