squeeze theorem

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Pls answer part ii

Problem 2: Find limits using the squeeze theorem
The squeeze theorem is a theorem used in calculus to evaluate a limit of a function.
The theorem is particularly useful to evaluate limits where other techniques might be unnecessarily
complicated.
i)
Research what the Squeeze Law is and write a brief summary using your own words.
i1)
The sequence {a,} is an infinite sequence (i.e n → 0) and satisfies the inequality such that
2n²-7
< an
3n²+8 for all positive integers n.
4n+5
6n-1
Зпап
Apply the squeeze theorem to find lim
by answering the following questions.
n-o (n+1)2
3nan
1)
Write an inequality for
(n+1)
2)
Use either numerical or graphical methods to estimate limits for each of the functions
on either side of the inequality in part a).
3nan
3)
Hence find lim
n-0o (n+1)2
Transcribed Image Text:Problem 2: Find limits using the squeeze theorem The squeeze theorem is a theorem used in calculus to evaluate a limit of a function. The theorem is particularly useful to evaluate limits where other techniques might be unnecessarily complicated. i) Research what the Squeeze Law is and write a brief summary using your own words. i1) The sequence {a,} is an infinite sequence (i.e n → 0) and satisfies the inequality such that 2n²-7 < an 3n²+8 for all positive integers n. 4n+5 6n-1 Зпап Apply the squeeze theorem to find lim by answering the following questions. n-o (n+1)2 3nan 1) Write an inequality for (n+1) 2) Use either numerical or graphical methods to estimate limits for each of the functions on either side of the inequality in part a). 3nan 3) Hence find lim n-0o (n+1)2
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