x2 +y x , f X = e-1/(x2+y2) = 0 (j) f (e) f 1 x + y -x y 9. Suppose f: R" R" is continuous and Xo is arbitrary. Define a sequence by xk f(Xk-1), k 1, 2,.... Prove that if x a, then f (a) = a. We say a is a fixed point of f. 10. Use Exercise 9 to find the limit of each of the following sequences of points in R, presuming it exists.
x2 +y x , f X = e-1/(x2+y2) = 0 (j) f (e) f 1 x + y -x y 9. Suppose f: R" R" is continuous and Xo is arbitrary. Define a sequence by xk f(Xk-1), k 1, 2,.... Prove that if x a, then f (a) = a. We say a is a fixed point of f. 10. Use Exercise 9 to find the limit of each of the following sequences of points in R, presuming it exists.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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