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Numerical Methods

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Question 40

The curve C C\,C has the equation y=(14−x)ln⁡xx>0y = (14 - x) \ln x \quad x > 0y=(14−x)lnxx>0

a.

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

[3]
b.

C C\,C has a stationary point at PPP. Show that the x x\,x coordinate of P P\,P lies between 5 and 5.5

[2]
c.

Show that the x x\,x coordinate of P P\,P is a solution of x=141+ln⁡x\displaystyle x = \frac{14}{1 + \ln x}x=1+lnx14​

[3]
d.

Use the iteration formula xn+1=141+ln⁡xn\displaystyle x_{n+1} = \frac{14}{1 + \ln x_n}xn+1​=1+lnxn​14​ with x0=5.25x_0 = 5.25x0​=5.25 to find, to 3 decimal places, the values of x1,x2 x_1, x_2\,x1​,x2​ and x3x_3x3​.

[3]
Markscheme

Numerical Methods Questions

  1. A Level
  2. /Maths
  3. /Numerical Methods

329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.

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