Let x* be the positive real root of 2sinx = x
(1) Show that T(x) = 2sinx is a λ-contraction on [π/2,2] ( and find λ)
(2) Find an n such that │T^n(π/2) – x*│<10^(-12) (and prove it)
in (1), i have to show that there is a constant λ satisfying
d(2sinx, 2siny)≤λd(x,y) right ?
here, how do i define d(2sinx, 2siny) ?
and in (2), does T^n mean composition of the function T of n times?
help me , please ,,, T_T
thanks a lot in advance