f(x)=ex+2+x−10f(x) = e^{x+2} + x - 10f(x)=ex+2+x−10
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=ln(10−x)−2x = \ln(10 - x) - 2x=ln(10−x)−2
Use the iteration formula xn+1=ln(10−xn)−2x_{n+1} = \ln(10 - x_n) - 2xn+1=ln(10−xn)−2 with x0=0.5x_0 = 0.5x0=0.5 to find, to 3 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
By choosing a suitable interval, prove that α=0.275\alpha = 0.275α=0.275 to 3 decimal places
