g(x) = x² − 3x − 5

a. Show that the equation g(x) = 0 can be written as x = √3x + 5.

b. Sketch on the same axes the graphs of y = x and y =  √3x+ 5.

c. Use your diagram to explain why the iterative formula x_{n + 1} = √3x_n + 5 converges to a root of g(x) when x₀ = 1. g(x) = 0 can also be rearranged to form the iterative formula

d. With reference to a diagram, explain why this iterative formula diverges when x₀ = 7. 

Transcribed Image Text:

Xn+1 = x-5 3