let y=f(X) be a uniformly continuous function on a set I. then for a given sequence (a_n)_{n∈N} ⊆ I , which of the following statement or statements is/are correct ? a-if (a_n) is Cauchy, then (f(a_n)) is also a Cauchy sequence. b- if (a_n) is convergent, then (f(a_n)) is also a Convergent sequence. c- y=f(X) is continuous at every point of the set I. d-all of the above. e- none of the above.
let y=f(X) be a uniformly continuous function on a set I. then for a given sequence (a_n)_{n∈N} ⊆ I , which of the following statement or statements is/are correct ? a-if (a_n) is Cauchy, then (f(a_n)) is also a Cauchy sequence. b- if (a_n) is convergent, then (f(a_n)) is also a Convergent sequence. c- y=f(X) is continuous at every point of the set I. d-all of the above. e- none of the above.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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let y=f(X) be a uniformly continuous function on a set I. then for a given sequence (a_n)_{n∈N} ⊆ I , which of the following statement or statements is/are correct ?
a-if (a_n) is Cauchy, then (f(a_n)) is also a Cauchy sequence.
b- if (a_n) is convergent, then (f(a_n)) is also a Convergent sequence.
c- y=f(X) is continuous at every point of the set I.
d-all of the above.
e- none of the above.
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