Answered: (Sequential Criterion for Continuity)… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 62E

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(Sequential Criterion for Continuity) Let (S₁, d₁) and (S2, d2) be metric spaces, and
f: S₁ S₂ be a function. Show that f is continuous at the point c E S₁ if and only
if for every sequence (xn) in S₁ that converges to c, the sequence f(xn) converges to
f(c). (Please use the correct definitions to prove this theorem.)

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