3. [2+1+1pt] Let g be defined on [5/8, 11/8].

g(x) = x +0.8 sin ..

(a) Determine the (smallest possible) Lipschitz constant L.

(b) How many iterations are required to increase the accuracy by a factor of 100, i.e., given some

To € [5/8, 11/8], what must & be such that you can guarantee that |æk-E| ≤ 10-²|xo-§|?

(c) Starting with initial guess = 5/8, compute the first fixed point iterate ₁ and use it,

together with the Lipschitz constant you found, to compute after how many fixed point

iterations k you can be certain that |- £k| < 10-¹⁰.

[1+1+1+1nt] The equation