x2 +yx, fX= e-1/(x2+y2)= 0(j) f(e) f1x + y-xy9. 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 itexists.

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Asked Aug 16, 2019
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I need help for problem 9. Thanks!

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.
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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.

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