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Pixel

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Posts posted by Pixel

  1. You are taking a limit so you can avoid [math] \frac{0}{0} [/math].

     

    Remember [math] h \rightarrow 0 [/math] means that [math] h [/math] is approaching (or tends to) [math] 0 [/math] and should not be simply substituted in.

     

     

     

    What you must remember is that you are trying to find the gradient of a tangent slope at a single point.

    The general idea behind what you are doing is: You need to make a secant line between two different points, if they were the same point you could not find the slope as you would have [math] \frac{0}{0} [/math]. This however does not give us an accurate tangent slope. To overcome this problem you let the distance between those two points approach 0 (so the slope of the secant line gets ever closer to the tangent slope you are looking for), and that is where taking the limit helps us.

     

    I suggest, as did the tree; go back and learn limits fully before trying to tackle the chain rule.

  2. There is a documentary called "Absolute Zero" that is very good.

     

    Another is "The Strange New World of Nanoscience" narrated by Stephen Fry. It's not terribly long, but still good.

     

    Last that I can think of is "Infinite Secrets of Archimedes". Which is all about a manuscript that was only found fairly recently (containing some interesting math from Archimedes).

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