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MA055G & MA056G |
Limits and Continuity
References
[RS] section 8.1
[HH] i kompendiet p. 47-51
[RS] section 8.2
[HH] i kompendiet p. 52-53
[RS] section 8.3-8.4
[RS] section 8.5
Lecture notes part 11 (available from course webpage).
Keywords
Definition of limit as x tends to infinity, definition of limit as x tends to x0. The Sandwich Theorem. Some techniques for computing limits, in particular for rational functions. Continuity. Presentation of some standard limits.
Introduction
In this block we shall start by considering what it means for a function to tend to a finite limit as x tends to infinity, and we gradually develop an understanding of the concept of a limit to inifinity by considering functions that do tend to a finite limit as x tends to infinity and some that do not. We use the Sandwich Theorem to compute some limits. After this we shall study the definition of limit as x tends to x0, limits from below and limits from above and coninuity. We gradually develop an understanding of the concept of a limit as x tends to x0 by studying the function sin(1/x) when x is close to 0. Next we show some rules of arithmetic for limits and some theorems that help us compute limits.
Reading
Read [RS] section 8.1, [HH] i kompendiet p. 47-51, [RS] section 8.2, [HH] i kompendiet p. 52-53, [RS] section 8.3-8.4 and [RS] section 8.5. These are covered by part 11 of the lecture notes and form block 6 of the course.
Exercises
Gränsvärden
- [RS] Testproblem 1 -2 (on p. 234), 3-4 (on p. 240), 5-7 (on p. 245), 8-9 (on p. 248), 10-12 (on p. 250)
- [WHGex] p. 54 i kompendiet: uppgift 49, 50, 51(a), 52(a)
- [RS] Övningar till kapitel 8 p. 250-252: 8.1(a)-(c), 8.2-8.4, 8.5(b)-(f), 8.6(a)-(c), 8.7(a)-(d), 8.8-8.9, 8.10-8.13, 8.15-8.16.
This is the 1st Edition of the study guide for Block 6 of the introduction course in mathematics, written by
Pia Heidtmann in 2008.
The study guide may be printed for personal use by
anybody with an interest.
This study guide and any parts of it and any previous and future versions of it must not
be copied or disseminated in any printed or electronic form
or stored on any publicly accessible website other than
http://apachepersonal.miun.se/~piahei/intro/res/
without permission from the author.
The author welcomes comments and corrections via email.
All contributions incorporated in updates of the manuscript will be acknowledged.
MID SWEDEN UNIVERSITY
Department of Natural Sciences, Engineering and Mathematics
Mid Sweden University
SE-851 70 SUNDSVALL
Sweden