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79. Find the limit of the sequence /2, v2v 2, v2/2/2, 80. A sequence {a,} is given by aj = /2, a n+1 = v2 + a,. – I+up (a) By induction or otherwise, show that {an} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim,. an exists. (b) Find limno an. 81. Show that the sequence defined by an+1 = 3 1. un is increasing and a, < 3 for all n. Deduce that {a,} is conver- gent and find its limit. 82. Show that the sequence defined by a1 = 2 an+1 3 - ап satisfies 0 < a, <2 and is decreasing. Deduce that the sequence is convergent and find its limit. t. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). e Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

79. Find the limit of the sequence /2, v2v 2, v2/2/2, 80. A sequence {a,} is given by aj = /2, a n+1 = v2 + a,. – I+up (a) By induction or otherwise, show that {an} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim,. an exists. (b) Find limno an. 81. Show that the sequence defined by an+1 = 3 1. un is increasing and a, < 3 for all n. Deduce that {a,} is conver- gent and find its limit. 82. Show that the sequence defined by a1 = 2 an+1 3 - ап satisfies 0 < a, <2 and is decreasing. Deduce that the sequence is convergent and find its limit. t. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). e Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

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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79. Find the limit of the sequence /2, v2v 2, v2/2/2, 80. A sequence {a,} is given by aj = /2, a n+1 = v2 + a,. – I+up (a) By induction or otherwise, show that {an} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim,. an exists. (b) Find limno an. 81. Show that the sequence defined by an+1 = 3 1. un is increasing and a, < 3 for all n. Deduce that {a,} is conver- gent and find its limit. 82. Show that the sequence defined by a1 = 2 an+1 3 - ап satisfies 0 < a, <2 and is decreasing. Deduce that the sequence is convergent and find its limit. t. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). e Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Transcribed Image Text:79. Find the limit of the sequence /2, v2v 2, v2/2/2, 80. A sequence {a,} is given by aj = /2, a n+1 = v2 + a,. – I+up (a) By induction or otherwise, show that {an} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim,. an exists. (b) Find limno an. 81. Show that the sequence defined by an+1 = 3 1. un is increasing and a, < 3 for all n. Deduce that {a,} is conver- gent and find its limit. 82. Show that the sequence defined by a1 = 2 an+1 3 - ап satisfies 0 < a, <2 and is decreasing. Deduce that the sequence is convergent and find its limit. t. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). e Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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