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x2+yx , J X = e-1/(2+y2) =0 x-,f (e) f (j)f xy -x y 9. Suppose f: R" R" is continuous and Xo is arbitrary. Define a sequence by X k = 1, 2, .. .. Prove that if x a, then f (a) a. We say a is a fixed point of f. = f(xk-1), 10. Use Exercise 9 to find the limit of each of the following sequences of points in R, presuming it exists. 1 (c) xo 1, xk = 1 + Xk-1 V2Xk-1 *(a) xo= 1, xk 2 1 *(d) xo 1, xk = 1 T 1 +Xk-1 Xk-1 + 2 (b) xo 5, x = 1 Xk-1 11. Give an example of a discontinuous function f: R - R having the property that for every c e R the level set f({c}) is closed.

x2+yx , J X = e-1/(2+y2) =0 x-,f (e) f (j)f xy -x y 9. Suppose f: R" R" is continuous and Xo is arbitrary. Define a sequence by X k = 1, 2, .. .. Prove that if x a, then f (a) a. We say a is a fixed point of f. = f(xk-1), 10. Use Exercise 9 to find the limit of each of the following sequences of points in R, presuming it exists. 1 (c) xo 1, xk = 1 + Xk-1 V2Xk-1 *(a) xo= 1, xk 2 1 *(d) xo 1, xk = 1 T 1 +Xk-1 Xk-1 + 2 (b) xo 5, x = 1 Xk-1 11. Give an example of a discontinuous function f: R - R having the property that for every c e R the level set f({c}) is closed.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 9 is included in this picture.

I only need help for problem 10c. Thank you very much!

x2+yx , J X = e-1/(2+y2) =0 x-,f (e) f (j)f xy -x y 9. Suppose f: R" R" is continuous and Xo is arbitrary. Define a sequence by X k = 1, 2, .. .. Prove that if x a, then f (a) a. We say a is a fixed point of f. = f(xk-1), 10. Use Exercise 9 to find the limit of each of the following sequences of points in R, presuming it exists. 1 (c) xo 1, xk = 1 + Xk-1 V2Xk-1 *(a) xo= 1, xk 2 1 *(d) xo 1, xk = 1 T 1 +Xk-1 Xk-1 + 2 (b) xo 5, x = 1 Xk-1 11. Give an example of a discontinuous function f: R - R having the property that for every c e R the level set f({c}) is closed.
Transcribed Image Text:x2+yx , J X = e-1/(2+y2) =0 x-,f (e) f (j)f xy -x y 9. Suppose f: R" R" is continuous and Xo is arbitrary. Define a sequence by X k = 1, 2, .. .. Prove that if x a, then f (a) a. We say a is a fixed point of f. = f(xk-1), 10. Use Exercise 9 to find the limit of each of the following sequences of points in R, presuming it exists. 1 (c) xo 1, xk = 1 + Xk-1 V2Xk-1 *(a) xo= 1, xk 2 1 *(d) xo 1, xk = 1 T 1 +Xk-1 Xk-1 + 2 (b) xo 5, x = 1 Xk-1 11. Give an example of a discontinuous function f: R - R having the property that for every c e R the level set f({c}) is closed.
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