WEBVTT
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We're trying to find the limit as X approaches infinity
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of the function. And as normal, we are
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going to want to take the natural log of both
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sides to put it in a simpler form. That
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simpler form is going to be the natural log of
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two times the natural log of X divided by one
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plus the natural log of X. Then when we
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evaluate this at infinity we get infinity over infinity.
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This is an indeterminate form. So we're going to
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want to use low tells rule when we do this
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in the numerator will get Natural log of two times
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one over X. And then in the denominator we
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will just get one over X. So if that
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one over acts in one of our X will cancel
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out giving us just natural log of two as a
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result. Um So now that we know that's natural
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log of two, we also know that the natural
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log of why? Because we had to take the
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natural log of both sides. So we have that
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the natural log of Y equals the natural log of
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two. Based on that, it's clear that why
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is going to be equal to two? So chew
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is our final answer.