Newtons Method Question (1 Viewer)

[johnnypaul]

Hi can someone please help me with a question involving Newton's method.
This is a question from the New Senior Mathematics 3 Unit book - Exercise 27(e) q11.

Use Newton's method to find approximatelt the value of:
11a) 3√10

Thanks

 

[Affinity]

3*sqrt(10) = sqrt(90)
basically, one wants x such that x^2 = 90
so the question amounts to solving x^2=90 or f(x)=x^2-90=0
f'(x)=2x

now ones knows that 10^2 = 100, so one can use that as an initial guess for x

x[0] = 10
x[1] = x[0] - f(x[0])/f'(x[0]) = 10 - 10/20 = 9.5
x[2] = x[1] - f(x[1])/f'(x[1]) = 9.486842....
...
continue till you are satisfied with the number of iterations

you get 3*sqrt(10) ~ 9.48683298.....