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1.9 Numerical Methods (A-level only)

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Question 58

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

1.9 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9 Numerical Methods (A-level only)

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.

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