Let ƒ : [−1,1] → R be a continuous function. Prove that the sequence (n) defined inductively by Xn 1 2n 1+|xn| Xn+1 = Xn+ ƒ( x₁ = 0, converges. You may use theorems from the lecture as long as you state them explicitly.

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 33E
icon
Related questions
Question
(c) Let ƒ : [−1,1] → R be a continuous function. Prove that the sequence (™)
defined inductively by
1
Xn+1 = Xn + 2nf (
Xn
1+|xn|
x1 = 0,
converges. You may use theorems from the lecture as long as you state them
explicitly.
Transcribed Image Text:(c) Let ƒ : [−1,1] → R be a continuous function. Prove that the sequence (™) defined inductively by 1 Xn+1 = Xn + 2nf ( Xn 1+|xn| x1 = 0, converges. You may use theorems from the lecture as long as you state them explicitly.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage