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1.9 Numerical Methods (A-level only)

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Question 45

It is given that

f(x)=x3+3x2−2xf(x) = x^3 + 3x^2 - 2\sqrt{x}f(x)=x3+3x2−2x​, x>0x > 0x>0

a.

Show that f(x)=0f(x) = 0f(x)=0 has a root in the interval [0.6,0.7][0.6, 0.7][0.6,0.7].

[2]
b.

Find f′(x)f'(x)f′(x).

[2]
c.

Starting with x0=0.65x_0 = 0.65x0​=0.65, apply the Newton-Raphson procedure once to find an approximate solution of f(x)=0f(x) = 0f(x)=0. Give your answer to three decimal places.

[2]
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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