Skip to content

Course home

Sign up

Numerical Methods

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223
Question 182

The equation x3−3x2+5=0x^3 - 3x^2 + 5 = 0x3−3x2+5=0 has exactly one real root.

a.

Show that, for this equation, the Newton-Raphson formula can be written

xn+1=2xn3−3xn2−53xn2−6xn x_{n+1} = \frac{2x_n^3 - 3x_n^2 - 5}{3x_n^2 - 6x_n} xn+1​=3xn2​−6xn​2xn3​−3xn2​−5​
[3]
b.

Using the formula given in part (a) with x1=−1x_1 = -1x1​=−1, find the values of x2 x_2\,x2​ and x3x_3x3​

[2]
c.

Explain why, for this question, the Newton-Raphson method cannot be used with x1=0x_1 = 0x1​=0

[1]
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