If D is a subset of R and c is a cluster point of D, implies which of the following? (a) N*(c, 1/n) D# Ø for any nEN. (b) c is an interior point of D (c) c is a boundary point of D (d) N(c,) contains infinitely many points of D. (e) c is in the closure of D.(

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.2: Integral Domains And Fields
Problem 16E: Prove that if a subring R of an integral domain D contains the unity element of D, then R is an...
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If D is a subset of R and c is a cluster point of D, implies which of the following?
(a) N*(c,1/n) N D ‡ Ø for any nEN.
(b) c is an interior point of D
(c) c is a boundary point of D
(d) N(c,) contains infinitely many points of D.
(e) c is in the closure of D.(
15
To prove that the limit of f(x)=x^2+4x as x approaches 2 is 12, given any >>0,
choose >0 such that d=min{4,k}. What is k?(¹ -
Transcribed Image Text:If D is a subset of R and c is a cluster point of D, implies which of the following? (a) N*(c,1/n) N D ‡ Ø for any nEN. (b) c is an interior point of D (c) c is a boundary point of D (d) N(c,) contains infinitely many points of D. (e) c is in the closure of D.( 15 To prove that the limit of f(x)=x^2+4x as x approaches 2 is 12, given any >>0, choose >0 such that d=min{4,k}. What is k?(¹ -
Which of the following sequences in R is convergent?
(a) x_n= n + (3/n)
(b) x_n= -1 + ( [(-1)^n]/n)
(c) x_n= sin(n*pi/2)
(d) x_n= n! / (3^n)
(e) x_n=n / In n(1·
18
The sequence whose nth term is given by x_n=sin(n*pi/6 (
Transcribed Image Text:Which of the following sequences in R is convergent? (a) x_n= n + (3/n) (b) x_n= -1 + ( [(-1)^n]/n) (c) x_n= sin(n*pi/2) (d) x_n= n! / (3^n) (e) x_n=n / In n(1· 18 The sequence whose nth term is given by x_n=sin(n*pi/6 (
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