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This is problem number seventy two of the sewer calculus
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eighth edition, section two point six for the limit
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. The limit is ex purchase infinity one minus three
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X divided by square root of the quantity X squared
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plus one equals three. Kill a street definition seven
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By finding values bin they correspond to absolutely cools to
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Sierra point one and absolutely equals to zero point zero
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fighters. And our definition, it has to do
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with defining there that the difference between the function and
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its limit the distance between the two or the absolute
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value be less than the value Absalon provided that you
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have an ex and greater than a certain value and
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right to the school together. And in our case
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, this is our function If and this is our
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limit own All right. So we need to find
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about you end that essentially guarantees of the function is
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less than Absalon away from the limit. So take
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a look at this function and we plant this function
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here one minus three x divided by the square root
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of the quantity X squared plus one. Ah,
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and we see that dysfunction approaches approaches Negative three.
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But we know that as the limit is, X
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approaches. Infinity Little, many calls native. Three
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. That means it'LL person ing into three but never
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be equal to negative three. So, really,
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when we're solving this problem here that we want the
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function to be within point one of its limit.
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Ah, that's exactly what determines our in. So
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within point one of negative three Centenary goes beyond negative
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three or equals negative three within point one means negative
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two point nine of negative three Thank you two point
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. And is Sarah quaint one away from negative three
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. So you need a next value at least equal
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to eleven point three to be able to achieve a
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value on the function within a zero point one of
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the limit, which is equal to make it three
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. So for this first step, Swan Lun is
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eleven point three Now. As we hit more precise
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with our Absalon point o five, we expect the
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larger Valley event how much more strict, stricter value
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. And that's exactly what we've seen. The function
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. It's causing negative three as we continued to the
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extraction and we need an X X value at least
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equal to twenty one point four In order to be
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within a point, there are five over the limit
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. So for this Absalon, our numbers approximately twenty
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one point four.