Intermediate Analysis - Lec 1 Real Analysis PDF

Title	Intermediate Analysis - Lec 1 Real Analysis
Course	Intermediate Analysis
Institution	University of Houston
Pages	14
File Size	687.8 KB
File Type	PDF
Total Downloads	32
Total Views	143

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Summary

Intermediate Analysis - Lec 1 Real Analysis...

Description

Real Analysis Two fundamental questions

1. What does it mean for a sequence to have a limit? 2. What does it mean for a function to have a limit?

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Chapter 4 preview... What is the limit of the following sequence of real numbers? 2.0000000 1.5000000 1.2500000 1.1250000

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Chapter 4 preview... Let’s list more terms... 2.0000000 1.5000000 1.2500000 1.1250000 1.0625000 1.0312500 1.0156250 1.0078125

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Chapter 4 preview... 1 Formula for the n-th term: 1 + n−1 2 2.0000000 1.5000000 1.2500000 1.1250000 1.0625000 1.0312500 1.0156250 1.0078125

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Chapter 4 preview... How do we define precisely what it means for this sequence to have a limit?

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Chapter 4 preview... How do we define precisely what it means for this sequence to have a limit?

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Chapter 4 preview... What about this sequence...? 2.0000000 1.6666666 1.5555555 1.5000000 1.4666666 1.4444444 1.4285714 1.4166666

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Chapter 4 preview...

F

4 +2

Chapter 4 preview...

“sn has a limit of 1” means: For any positive number ǫ > 0, there is some positive integer N such that: If n > N , then |sn − 1| < ǫ.

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