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1.(a) Prove that the sequence defined by x1= 3 and Xn+1 =1/4−xn
converges.
(b) Now that we know limxn exists, explain why limxn+1 must also exist
and equal the same value.
(c) Take the limit of each side of the recursive equation in part (a) of this
exercise to explicitly compute limxn.
2.Let x1= 2, and definexn+1 =1/2(xn+2/xn)

.
(a) Show that x上2下n is always greater than 2, and then use this to prove thatxn−xn+1 ≥ 0. Conclude that limXn=√2.
(b) Modify the sequence (xn) so that it converges to √c.

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