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1.10 Numerical Methods (A-level only)

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Question 51

It is given that

f(x)=sin⁡2x+ln⁡xf(x) = \sin 2x + \ln xf(x)=sin2x+lnx, x>0 x > 0\,x>0

where x x\,x is measured in radians.

a.

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].

[3]
b.

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.

[4]
Markscheme

1.10 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.10 Numerical Methods (A-level only)

133 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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