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2. (a) Define what it means for a sequence (an) to have a limit. Give an example of a sequence that does not have a limit. (b) Assume that a sequence (a) has limit L. For the given value of ε, find a natural number N, such that lan-L N: 1 an= 2√√√π+1 with 0 and ε = 10-2 818 (c) Consider the sequence (an) defined recursively by a₁ = 10 and an+1 = √√√an +6 for all nЄ N. Show that: (i) an ≥ 3 for all nЄN, (ii) the sequence (an) is decreasing, (iii) the sequence (a) has a limit. Hence or otherwise, calculate lim an

2. (a) Define what it means for a sequence (an) to have a limit. Give an example of a sequence that does not have a limit. (b) Assume that a sequence (a) has limit L. For the given value of ε, find a natural number N, such that lan-L N: 1 an= 2√√√π+1 with 0 and ε = 10-2 818 (c) Consider the sequence (an) defined recursively by a₁ = 10 and an+1 = √√√an +6 for all nЄ N. Show that: (i) an ≥ 3 for all nЄN, (ii) the sequence (an) is decreasing, (iii) the sequence (a) has a limit. Hence or otherwise, calculate lim an

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hi, could you solve this question? part a, b, and c.

2. (a) Define what it means for a sequence (an) to have a limit. Give an example of a sequence that does not have a limit. (b) Assume that a sequence (a) has limit L. For the given value of ε, find a natural number N, such that lan-L<E for all n > N: 1 an= 2√√√π+1 with 0 and ε = 10-2
Transcribed Image Text:2. (a) Define what it means for a sequence (an) to have a limit. Give an example of a sequence that does not have a limit. (b) Assume that a sequence (a) has limit L. For the given value of ε, find a natural number N, such that lan-L<E for all n > N: 1 an= 2√√√π+1 with 0 and ε = 10-2
818 (c) Consider the sequence (an) defined recursively by a₁ = 10 and an+1 = √√√an +6 for all nЄ N. Show that: (i) an ≥ 3 for all nЄN, (ii) the sequence (an) is decreasing, (iii) the sequence (a) has a limit. Hence or otherwise, calculate lim an
Transcribed Image Text:818 (c) Consider the sequence (an) defined recursively by a₁ = 10 and an+1 = √√√an +6 for all nЄ N. Show that: (i) an ≥ 3 for all nЄN, (ii) the sequence (an) is decreasing, (iii) the sequence (a) has a limit. Hence or otherwise, calculate lim an
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