Oblique Asymptotes and finding them with Long Division
Channel: Paul King
Date: 2013-12-29

This video discusses the last topic in Rational Functions, which is at heart an optional topic, not strictly part of my course. Students are often curious about finding these, and it uses techniques that are already part of the course, albeit slightly differently. 

Students may find the idea of discarding a binomial with an x-term in it to be cavalier. I could give an explanation, but it might be better to defer that to another video. Once again, all of the reasons this is true can be shown entirely with concepts from Advanced Functions taken up in class. Before watching that video, you may want to take a few minutes to think about it on your own, first.

The play list: http://www.youtube.com/playlist?list=PLasIAjqJOqkLIkQ3UiSgnutUi24WRp7m6
Synthetic Division with Fractional Zeroes: http://www.youtube.com/watch?v=iK6iS80Mm6c&list=PLasIAjqJOqkLIkQ3UiSgnutUi24WRp7m6&index=2
Oblique asymptotes and finding them with long division: http://www.youtube.com/watch?v=YcHI_UppicQ&list=PLasIAjqJOqkLIkQ3UiSgnutUi24WRp7m6&index=3
Oblique asymtotes: Why discard the remainder? http://www.youtube.com/watch?v=jZuZGvUgQj8&list=PLasIAjqJOqkLIkQ3UiSgnutUi24WRp7m6&index=4
Curve Sketching with Rational Functions: http://youtu.be/vgyQMC9Nm_M
Cauchy's Continuity: http://youtu.be/tBuxWO3Hfr0
Introduction to Piecewise Functions: http://youtu.be/GqwlV_KWkBE
Piecewise Functions, Jump Discontinuities, and Limits: http://youtu.be/nyJDuYyfPEQ

VIdeos relevant to trignometry:
Review of Trigonometry: http://youtu.be/mh-x3kNkrhY

Videos relevant to logarithms and exponential functions:
Exponent Laws: http://youtu.be/eIk26nr7ktg
Scientific Notation: http://youtu.be/uZ0ETyx2DkQ
Solving Logarithmic Equations: http://youtu.be/0rcPDgg-BoI

For the techies among you, this video was shot using an el-cheapo Panasonic HMX-F80 I got from an open-box sale for 100 bucks. It stores video in MP4 format. The post-production was done entirely in Linux Ubuntu Studio 13.10 using entirely open-source software, and where practical, open formats such as ogg vorbis were chosen. Voice tracks were recorded using Audacity. The microphone used is part of an inexpensive but good-quality Logitech G330 gaming headset.