n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1) (ii) 8n(x) = f(x) = = Find the limit function of {gn}, if exists. 1 -2' Xn By using limit criterion. XER+. explain whether {n} Converges uniformly on By using Cauchy criterion for uniform convergence.

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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3b

Let the function f: R→ R be defined by
1
x2,
f(x) =
=
0,
x=0,
x = 0.
Transcribed Image Text:Let the function f: R→ R be defined by 1 x2, f(x) = = 0, x=0, x = 0.
n
For each n EN, consider x = - with x ER+. Define the sequence {gn} by
X
8n(x) = f(xn) =
(a) Find the limit function of {gn}, if exists.
(b)
A = [1,2) CR+.
(1)
(ii)
1
x²
By using limit criterion.
XER+.
explain whether {gn} Converges uniformly on
By using Cauchy criterion for uniform convergence.
Transcribed Image Text:n For each n EN, consider x = - with x ER+. Define the sequence {gn} by X 8n(x) = f(xn) = (a) Find the limit function of {gn}, if exists. (b) A = [1,2) CR+. (1) (ii) 1 x² By using limit criterion. XER+. explain whether {gn} Converges uniformly on By using Cauchy criterion for uniform convergence.
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