WEBVTT
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this's problem or forty two of the Stuart Calculus,
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either edition section two point four prove using definition six
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. That the limit is experts is negative. Three
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of the function one over the quantity X plus three
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to the fourth power. It's called an identity.
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So definition six states that for any m greater than
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zero there exists a delta grid. Isn't zero such
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that if the absolute value of the difference between X
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and me is Liston daughter, then the function is
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guaranteed to be great with them. So we just
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being with second inequality and see what relationship we confined
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between them and Delta. So our function this one
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over the quantity X plus three to the fourth and
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we want to guarantee that this greater than any value
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we choose for them. We re arrange this one
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over him created than the quantity express T to the
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fourth. And then we take ah, the forth
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route to put science And here the forth route cancel
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. And what we're left with is that the quantity
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extra story must be less Stan the must be listen
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one over the forth route of him. If we
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recall the conditional for Delta Is that expectancy or in
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this case, Xmas Negative three. Must be.
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This difference was fearless and Delta and And we re
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write it this way. You can see that Delta
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and this term here. Ah, having value equal
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to that is an appropriate choice that guarantees bad for
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any delta. Are you can find any delta for
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any given value? Mm. For example. Mmm
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is ten thousand. The four three ten thousand is
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ten. So choosing the delta equal to one over
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ten. Ah provide prevents the conditions needed to prove
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this limit. So for any value, them there
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exists a daughter, and therefore the positive values and
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the both correspond to these inequalities. And everything is
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consistent there forthis summit as expressing it. Three of
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dysfunction, unequal to infinity.