Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let {f} be a sequence of continuous functions which converges uniformly to a function f on a set SC R. Let {xn} ≤ S be a sequence converging to x € S. Prove that lim fn(x) = f(x). n→∞ Is this statement true if we assume fn → f pointwise? Why?

Let {f} be a sequence of continuous functions which converges uniformly to a function f on a set SC R. Let {xn} ≤ S be a sequence converging to x € S. Prove that lim fn(x) = f(x). n→∞ Is this statement true if we assume fn → f pointwise? Why?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 64E
See similar textbooks
icon
Related questions
Question

Could you explain how to do this in detail?

Let {f} be a sequence of continuous functions which converges uniformly to a function f on a set SCR. Let {n} S be a sequence converging to x E S. Prove that lim fn(x) = f(x). n- Is this statement true if we assume fn → f pointwise? Why?
Transcribed Image Text:Let {f} be a sequence of continuous functions which converges uniformly to a function f on a set SCR. Let {n} S be a sequence converging to x E S. Prove that lim fn(x) = f(x). n- Is this statement true if we assume fn → f pointwise? Why?
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
SEE MORE TEXTBOOKS