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3.7 Numerical methods (A-level only)

3.7 Numerical methods (A-level only)

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Question 37

The curve C C\,C has the equation y=(6−x)ln⁡xy = (6 - x) \ln xy=(6−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 2.5 and 3.

[3]
c.

Show that the xxx-coordinate of P P\,P is a solution of x=61+ln⁡x\displaystyle x = \frac{6}{1 + \ln x}x=1+lnx6​.

[3]
d.

Use the iteration formula xn+1=61+ln⁡xn\displaystyle x_{n+1} = \frac{6}{1 + \ln x_n}xn+1​=1+lnxn​6​ with x0=2.8x_0 = 2.8x0​=2.8 to find, to 3 decimal places, the values of x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​.

[3]
Markscheme

3.7 Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7 Numerical methods (A-level only)

125 exam-style questions on CCEA A Level Maths 3.7 Numerical methods (A-level only), covering 3.7.1 Numerical methods (A-level only), 3.7.2 Numerical methods (A-level only), 3.7.3 Numerical methods (A-level only), and 3.7.4 Numerical methods (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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