(a) Let a1 = a, a2 = f(a), a3 = f(a2) = f(f(a)), . . . an+1...

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(a) Let a1 = a, a2 = f(a), a3 = f(a2) = f(f(a)), . . . an+1 = f(an), where f is a continuous function. If, limn→∞ an = L show that f(L) = L.
(b) Illustrate part (a) by taking f(x) = cos x, a = 1, and estimating the value of L to five decimal places.
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