If(2) -f(w)| < j-비, Va,yER. a. Show that f is a continuous function on R. b. Let zo = 1, z, = f(Tn 1), n 2 1. Use the Comparison Test to show that E("n – In-1) converges absolutely, and conclude that lim In exists.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Let f be a function defined on R satisfying
|f(x) – f(y)| < -1z – y|, Vz, y E R.
a. Show that f is a continuous function on R.
b. Let zo = 1, z, = f(Tn_1), n > 1. Use the Comparison Test to show that
(In – In-1)
converges
and conclude that
lim In
exists.
c. Let r, be the limit of (zn). Show that a, =
= f(x.).
Transcribed Image Text:Let f be a function defined on R satisfying |f(x) – f(y)| < -1z – y|, Vz, y E R. a. Show that f is a continuous function on R. b. Let zo = 1, z, = f(Tn_1), n > 1. Use the Comparison Test to show that (In – In-1) converges and conclude that lim In exists. c. Let r, be the limit of (zn). Show that a, = = f(x.).
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