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1.1 Explain the difference between an accumulation point and a limit. 1.2 If lim a, = x and lim yn = y, then show formally that lim(xn + Yn) = x+y.

1.1 Explain the difference between an accumulation point and a limit. 1.2 If lim a, = x and lim yn = y, then show formally that lim(xn + Yn) = x+y.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 1 1.1 Explain the difference between an accumulation point and a limit. 1.2 If lim an = x and lim y, = y, then show formally that lim(xm + Yn) = x + y. 1.3 Consider the following sequences: (-1)n-1 Xn = n {yn}=1 yn = ' (n)² 11 n +1 (a) Does the sequence {y,n} converge to a limit or not? Calculate the limit (if it exists) and the accumulation point(s) (if it exists).
Transcribed Image Text:Question 1 1.1 Explain the difference between an accumulation point and a limit. 1.2 If lim an = x and lim y, = y, then show formally that lim(xm + Yn) = x + y. 1.3 Consider the following sequences: (-1)n-1 Xn = n {yn}=1 yn = ' (n)² 11 n +1 (a) Does the sequence {y,n} converge to a limit or not? Calculate the limit (if it exists) and the accumulation point(s) (if it exists).
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