Comments on: Why Do We Need Limits and Infinitesimals? http://betterexplained.com/articles/why-do-we-need-limits-and-infinitesimals/ Learn Right, Not Rote. Wed, 16 May 2012 12:30:32 +0000 hourly 1 http://wordpress.org/?v= By: Calculus: Building Intuition for the Derivative | BetterExplained http://betterexplained.com/articles/why-do-we-need-limits-and-infinitesimals/#comment-65509 Calculus: Building Intuition for the Derivative | BetterExplained Thu, 29 Mar 2012 11:09:42 +0000 http://betterexplained.com/?p=380#comment-65509 [...] The magic’s in the final step: how do we remove the electrodes? We have two approaches: [...] [...] The magic’s in the final step: how do we remove the electrodes? We have two approaches: [...]

]]> By: Kalid http://betterexplained.com/articles/why-do-we-need-limits-and-infinitesimals/#comment-5920 Kalid Thu, 11 Aug 2011 08:42:14 +0000 http://betterexplained.com/?p=380#comment-5920 @werterber: Not a silly question at all! In my head, it's saying "what's the ratio of width [cos(x)] to distance traveled (x)". As our distance traveled goes to 0 (we aren't moving from the starting point), cos(x) tends towards 1 -- we're pretty much at the same width. So it becomes "1 / 0" in my head. @werterber: Not a silly question at all! In my head, it’s saying “what’s the ratio of width [cos(x)] to distance traveled (x)”.

As our distance traveled goes to 0 (we aren’t moving from the starting point), cos(x) tends towards 1 — we’re pretty much at the same width. So it becomes “1 / 0″ in my head.

]]> By: werterber http://betterexplained.com/articles/why-do-we-need-limits-and-infinitesimals/#comment-5919 werterber Thu, 11 Aug 2011 08:24:29 +0000 http://betterexplained.com/?p=380#comment-5919 Hello, i have silly question. How intuitively explain that cos x/x is undefind? There is graf> http://www.wolframalpha.com/input/?i=Plot%5B{cos%5Bx%5D%2C+x}%2C+{x%2C+-1.0%2C+1.0}%5D thx Hello, i have silly question. How intuitively explain that cos x/x is undefind?
There is graf> http://www.wolframalpha.com/input/?i=Plot%5B{cos%5Bx%5D%2C+x}%2C+{x%2C+-1.0%2C+1.0}%5D

thx

]]> By: Kalid http://betterexplained.com/articles/why-do-we-need-limits-and-infinitesimals/#comment-5918 Kalid Thu, 09 Jun 2011 00:29:53 +0000 http://betterexplained.com/?p=380#comment-5918 @Dave: Great question. I can't say I'm completely comfortable with limits, but I think you can jump back and forth (the Keisler Calculus book has some examples like this I believe). I think the bigger goal is to figure out what is being said, i.e. "What does this equation equal, within some level of tolerance?". Limits and infinitesimals are two ways to define that tolerance threshold, but infinitesimals are "easier" in that it's built in (and you don't need to explicitly define epsilon, delta, etc.). @Dave: Great question. I can’t say I’m completely comfortable with limits, but I think you can jump back and forth (the Keisler Calculus book has some examples like this I believe). I think the bigger goal is to figure out what is being said, i.e. “What does this equation equal, within some level of tolerance?”. Limits and infinitesimals are two ways to define that tolerance threshold, but infinitesimals are “easier” in that it’s built in (and you don’t need to explicitly define epsilon, delta, etc.).

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