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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 70

A research drone's vertical displacement yyy (in meters) from its starting altitude is modeled by the equation

y=2x2ln⁡(x)−5x,x>0.5 y = 2x^2 \ln(x) - 5x, \quad x > 0.5 y=2x2ln(x)−5x,x>0.5

where xxx is the horizontal distance in kilometers from the launch point. The drone reaches a minimum altitude at point PPP.

a.

Show, using calculus, that the xxx-coordinate of PPP is a solution of the equation

4xln⁡(x)+2x−5=0 4x \ln(x) + 2x - 5 = 0 4xln(x)+2x−5=0
[3]
b.

Using the Newton-Raphson method with f(x)=4xln⁡(x)+2x−5f(x) = 4x \ln(x) + 2x - 5f(x)=4xln(x)+2x−5 and a first approximation x1=2x_1 = 2x1​=2, find the value of x2x_2x2​ and the value of x3x_3x3​, giving your answers to 3 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)

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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