Let fn RR be a sequence of continuous functions which converg uniformly to a function f : R → R. Let (xn) be a sequence of re numbers which converges to x E R. Show that fn(n) → ƒ(x).
Let fn RR be a sequence of continuous functions which converg uniformly to a function f : R → R. Let (xn) be a sequence of re numbers which converges to x E R. Show that fn(n) → ƒ(x).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 65E
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![7. Let fn: R → R be a sequence of continuous functions which converges
uniformly to a function f : R → R. Let (n) be a sequence of real
numbers which converges to x E R. Show that fn(xn) → f(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F490cbcd2-ad81-426b-824f-903aced284ba%2F142f16fe-1155-4953-9de4-1a7511ba0e19%2F2ryqcmg_processed.png&w=3840&q=75)
Transcribed Image Text:7. Let fn: R → R be a sequence of continuous functions which converges
uniformly to a function f : R → R. Let (n) be a sequence of real
numbers which converges to x E R. Show that fn(xn) → f(x).
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