Let (x) = x 2 c and let e n = x n c be

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Let ƒ(x) = x² − c and let e_n= x_n − √c be the error in x_n.

(xn + c/xn) and en+1 = en/2xn. (a) Show that Xn+1 = (b) Show that if xo> c, then xn> e for all n. Explain

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Nov 26, 2023 03:05 AM

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Let (x) = x 2 c and let e n = x n c be

Question:

(xn + c/xn) and en+1 = en/2xn. (a) Show that Xn+1 = (b) Show that if xo> √c, then xn> √e for all n. Explain graphically. (c) Show that if xo> √c, then en+1 ≤ e²/(2√c).

Step by Step Answer:

a Let fx x c Then as long as xn 0 Now xn 1 Xn words en1 2 c ...View the full answer

Calculus

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