Skip to content

Course home

Sign up

Numerical Methods

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445
Question 17

The curve C C\,C has the equation y=(20−x)ln⁡xx>0y = (20 - x) \ln x \quad x > 0y=(20−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 6.5 and 7

[2]
c.

Show that the x x\,x coordinate of P P\,P is a solution of x=201+ln⁡x\displaystyle x = \frac{20}{1 + \ln x}x=1+lnx20​

[3]
d.

Use the iteration formula xn+1=201+ln⁡xn\displaystyle x_{n+1} = \frac{20}{1 + \ln x_n}xn+1​=1+lnxn​20​ with x0=6.75x_0 = 6.75x0​=6.75 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.

Question bank