WEBVTT
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all right, We're talking about the number e here
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Oilers number, and we want to start by talking
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about its definition. They're actually a couple of different
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definitions. It kind of depends on your context.
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So when you were in algebra two or pre calculus
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, you may have had some problems about compound interest
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, and you may have learned about E. At
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that time. And in that context, E's defined
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as the limit as n approaches or as X approaches
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, infinity of one plus one over X to the
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X power. Now that could be an and not
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an accent could be any letter. But in our
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book the calculus book, they define E in a
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different way because we're going to be interested in the
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context of calculus in slopes of tangent lines. So
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E is the number that when used as the base
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of an exponential function, So when put into an
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exponential function like this, he is the number that
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would yield a graph whose tangent line at the 0.1
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would have a slope of one. That's how he
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is being defined in this context. The approximate value
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V is 2.718 to 8. It's another one of
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those irrational numbers like Pi that just has a non
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repeating, non terminating decimal and the natural exponential function
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that was alluded to earlier. That is why equals
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E to the X And just like the other exponential
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functions we've been looking at, it would have a
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domain of all real numbers, and the range would
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be oops, that should say, are for range
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. The range would be numbers greater than zero,
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so zero to infinity.