Sequences II
3302 views
|
2
ratings
Lesson Description:
Precise definition of the limit of a sequence. Monotonicity and boundedness; convergence of bounded, monotonic sequences. Recursively defined sequences, fixed points, and web plots.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Questions answered by this video:
- What is the epsilon definition for the limit of a sequence?
- What does it mean for a sequence to be bounded?
- What is monotonicity?
- What does it mean for a sequence to be decreasing, increasing, nondecreasing, nonincreasing, strictly decreasing, and strictly increasing?
- What does it mean for a sequence to be monotonic?
- What does it mean for a sequence to be eventually monotonic?
- What is a recursively generated sequence?
- What is a fixed point of a sequence?
- What is a web plot of a sequence?
- How do you find the intersection between y = x and a sequence using a web plot?
- How can you tell if a sequence converges or diverges using a web plot?
- What is alternating convergence?
- How do you find the limit of a sequence using a web plot?
-
Staff Review
This video explains limits of sequences and shows that a limit is equal to a number in a way that is similar to what is done in an undergraduate Analysis course. Boundedness and monotonicity are also explained and shown with examples. Some really great examples are shown and explained. Web plots are shown with examples also.
