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| | #REDIRECT [[L'Hôpital's Rule]] | | #REDIRECT [[L'Hôpital's Rule]] |
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| − | Video by 3Blue1Brown: https://www.youtube.com/watch?v=kfF40MiS7zA
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| − | Text explanation:
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| − | let <math>z(x) = \frac{f(x)}{g(x)}</math> where <math>f(x)</math> and <math>g(x)</math> are both nonzero function with value <math>0</math> at point <math>a</math>
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| − | (for example, <math>g(x) = cos(\frac{\pi}{2} x)</math>, <math>f(x) = 1-x</math>, and <math>a = 0</math>.)
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| − | Note that the points surrounding z(a) aren't approaching infinity, as a function like <math>f(x) = 1/x-1</math> might at <math>f(a)</math>
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| − | The points infinitely close to z(a) will be equal to <math>\lim{b\to \infty} \frac{f(a+b)}{g(a+b)}</math>
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| − | Noting that <math>\lim{b\to \infty} f(x+b)</math> and <math>\lim{b\to \infty} g(x+b)</math> are equal to <math>f'(x)</math> and <math>g'(x)</math> respectively.
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| − | This means that the points approaching <math>\frac{f(x)}{g(x)}</math> at point a where <math>f(a)</math> and <math>g(a)</math> are equal to 0 are equal to $\frac{f'(x)}{g'(x)}
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