Use Newton's Method to estimate an intersection of the functions $f (x) = 5 x - 1$ and $g (x) = \tan x$ Use the initial estimate $x_{1} = 0.2628$
Find x_2 and x_3

Question

Use Newton's Method to estimate an intersection of the functionsf(x)=5x−1 and g(x)=tanx Use the initial estimate x_1=0.2628Find x_2 and x_3

Tom K. · Accepted Answer

We find the intersection of two functions by i subtracting one from the other and finding the 0s

The Newton method is x_n+1 = x_n - h(x_n)/h'(x_n)

h(x) = f(x) - g(x) = 5x - 1 - tan(x)

h'(x) = 5 - sec²(x)

Thus, x_n+1 = x_n - (5x_n - 1 - tan(x_n))/(5 - sec²(x_n))

x₂ = .251348

x₃ = .251358

Use Newton's Method to estimate an intersection of the functions f ( x ) = 5 x − 1 and g ( x ) = tan x Use the initial estimate x 1 = 0.2628 : x 1 = 0.2628