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1.10 Numerical Methods (A-level only)

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Question 3

The curve C C\,C has the equation y=(15−x)ln⁡xy = (15 - x) \ln xy=(15−x)lnx, x>0x > 0x>0.

a.

Find dydx\displaystyle \frac{dy}{dx}dxdy​

[3]
b.

C C\,C has a stationary point at PPP. Show that the xxx-coordinate of P P\,P lies between 5 and 6.

[3]
c.

Show that the xxx-coordinate of P P\,P is a solution of x=151+ln⁡x\displaystyle x = \frac{15}{1 + \ln x}x=1+lnx15​.

[3]
d.

Use the iteration formula xn+1=151+ln⁡xn\displaystyle x_{n+1} = \frac{15}{1 + \ln x_n}xn+1​=1+lnxn​15​ with x0=5.5x_0 = 5.5x0​=5.5 to find, to 3 decimal places, the values of x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​.

[3]
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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