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Question: numerical analysis let xn be a sequence of positive numbers...

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(Numerical Analysis)

Let xn be a sequence of positive numbers converging to zero. Show the following:

(a) If xn+1 = x2n, xn converges to 0 quadratically.

(b) If xn+1 = 1xn, xn converges to 0 linearly.2

(c) If xn+1 = n−n, xn converges to 0 superlinearly.

Let zn be a sequence of positive numbers converging to zero. Show the following: a) If xn+1 _ wn, wn converges to 0 quadratically. (b) If nt- jz, 2n converges to 0 linearly. (c) If xn+1-nn, xn converges to 0 superlinearly.

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