f(x) = 4 cot x 8x + 3, 0 < x < , where x is in radians. a. Show that there is a

f(x) = 4 cot x − 8x + 3, 0

a. Show that there is a root α of f(x) = 0 in the interval [0.8, 0.9].

b. Show that the equation f(x) = 0 can be written in the form 

c. Use the iterative formula

to calculate the values of x₁, x₂ and x₃ giving your answers to 4 decimal places.

d. By considering the change of sign of f(x) in a suitable interval, verify that α = 0.831 correct to 3 decimal places. 

X = COS X 2 sin x + 3 8