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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 16

f(x)=ln⁡(2x+1)+x2−5x>−0.5f(x) = \ln(2x + 1) + x^2 - 5 \quad x > -0.5f(x)=ln(2x+1)+x2−5x>−0.5

a.

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]

[2]
b.

Find f′(x)f'(x)f′(x)

[3]
c.

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.

[3]
Markscheme

1.10 Numerical Methods (A-level only) Questions

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

137 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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