Week #2
We'll start where we left off, at the tangent. Last week we took a careful look at the unit circle (centered at the origin) and several lines tangent to key points on this circle. A sequence of secant-slopes were then computed, and their computed values formed a predictable sequence. I hope you all agree that this sequence of secant-slopes moved towards our 'predicted' slope of the tangent.
This week we will look at the concept of limits, and we'll start with a predictable sequence that moves towards a fixed number. For example if we want to move towards one, from values smaller than one, a predictable sequence could be:
0.9, 0.99, 0.999, 0.9999, . . . , 0.9999999999, . . .
Or move towards one, from values bigger than one, a predictable sequence would be:
1.1, 1.01, 1.001, 1.001, . . . , 1.00000000001, . . .
You'll need a way to compute quickly, so please bring your calculators!
This week we will look at the concept of limits, and we'll start with a predictable sequence that moves towards a fixed number. For example if we want to move towards one, from values smaller than one, a predictable sequence could be:
0.9, 0.99, 0.999, 0.9999, . . . , 0.9999999999, . . .
Or move towards one, from values bigger than one, a predictable sequence would be:
1.1, 1.01, 1.001, 1.001, . . . , 1.00000000001, . . .
You'll need a way to compute quickly, so please bring your calculators!
posted by Ron Bannon at
9/11/2004 07:24:00 PM
6 Comments:
Okay, so you won't post, so what alternative does that leave me? I guess, like in any non-communicative relationship, I'll just have to talk to myself.
I've noticed that my fingers get twisted when I do lots of calculations on my handheld TI calculator, but it's still damn good at doing computation.
Consider this: "A single person using a hand-held calculator — without pausing to eat or sleep --- would need more than two million years to calculate what the Apple supercluster can calculate in a single second." So what does a super cluster of G5s look like? Well, I'd say it might be pretty hard to carry such a massive piece of hardware around.
Calculators, consider yourself lucky to have one. However, don't ever think that real-world computations can be done as quickly as a cluster.
By
Ron Bannon, at 12:52 PM
Stewart's textbook comes with two CDs, or at least mine did. One is called TEC, and the other is an interactive video skills builder. The videos are basically problems with narration, very well done examples, where you can take a interactive quiz at the end.
It might be a good idea to play with these.
By
Ron Bannon, at 5:56 PM
Okay, I just took at look at the TEC (Tools for Enriching Calculus) CD and it contains many basic web-based Java applications of important calculus concepts. Again, it's another resource that many of you may find helpful.
Oh, if you're interested in seeing free, carefully constructed web-based courseware, take a peek at MIT's wonderful mathematics OpenCourseWare.
By
Ron Bannon, at 6:17 PM
In visting your office to review the quiz material, i must say on quiz 1 question 1 I felt it was definitly a trick question. Overall as you explained the material to me, on quiz one, I realized my mistakes were careless. However it was definitly a pleasure having the material explained to me thoroughly. Thanks for your time
By
Anonymous, at 10:43 AM
I will of course try to be "less tricky" in the future. In fact, sometimes I even find my own questions to be trickier than I initially thought. To paraphrase Goeth (I think) "any fool can write an exam." And sometimes my questions are foolish.
More importantly: "He who does not know one thing knows another." -- Kenyan proverb
Kind of funny, don't you think?
By
Ron Bannon, at 12:47 PM
You don't have to register, but everyone should use their real name when posting. Anonymous is okay, but sigh the post.
-Ron Bannon
By
Anonymous, at 12:48 PM
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