Skip to content

Course home

Sign up

Numerical Methods

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223
Question 214

A research drone's vertical displacement yyy (in meters) from its starting altitude is modeled by the equation

y=2x2ln⁡(x)−5x,x>0.5 y = 2x^2 \ln(x) - 5x, \quad x > 0.5 y=2x2ln(x)−5x,x>0.5

where xxx is the horizontal distance in kilometers from the launch point. The drone reaches a minimum altitude at point PPP.

a.

Show, using calculus, that the xxx-coordinate of PPP is a solution of the equation

4xln⁡(x)+2x−5=0 4x \ln(x) + 2x - 5 = 0 4xln(x)+2x−5=0
[3]
b.

Using the Newton-Raphson method with f(x)=4xln⁡(x)+2x−5f(x) = 4x \ln(x) + 2x - 5f(x)=4xln(x)+2x−5 and a first approximation x1=2x_1 = 2x1​=2, find the value of x2x_2x2​ and the value of x3x_3x3​, giving your answers to 3 decimal places.

[4]
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