3 2 1 1pt let g be defined on 5 8 11 8 g x x 0 8 sin a determine the s
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
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