a. Show that the equation f(x) = 0 can be written as x = 1.5 − 0.5e^−0.8x. 

b. Use the iterative formula x_{n + 1} = 1.5 − 0.5e^−0.8x with x₀ = 1.3 to obtain x₁, x₂ and x₃. Hence write down one root of f(x) = 0 correct to 3 decimal places.

c. Show that the equation f(x) = 0 can be written in the form x = p ln (3 − 2x), stating the value of p.

d. Use the iterative formula x_{n + 1} = p ln (3 − 2x_n) with x₀ = −2.6 and the value of p found in part c to obtain x₁, x₂ and x₃. Hence write down a second root of f(x) = 0 correct to 2 decimal places.

Transcribed Image Text:

f(x) = 0.8.x. - 1 3- 2x' 3 2 , Xz;