WEBVTT
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we're gonna be taking the limit as X goes to
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infinity of X to the one over X. Um
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And we can simplify this by um considering the fact
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that if we plug in infinity we're going to get
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infinity to the power of zero. So since that's
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the indeterminate form, we're going to um take the
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natural log of both sides. When we do that
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, we'll end up getting at the natural log of
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Y equals one over X times the natural log of
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X, which is just the natural log of acts
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over X. Then putting infinity, we get infinity
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over infinity. So we must Take the derivative of
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both sides giving us one over X Right to Buy
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one. Now when we plug in infinity we will
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get one over infinity which is zero divided by one
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, which is zero. So zero is not our
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answer. Instead what we have. Is that the
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natural log of why equals zero is our answer.
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So let's solve for why we know that we can
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take E. To the power of both sides.
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Can I ask why equals E. To the power
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of zero? So based on this, we see
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that why is going to equal one? So one
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ends up being our final final answer. And this
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was through using a method by which we take the
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national log on both sides and then employ the hotel's
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rule.