El_Arrow
  • El_Arrow
don't understand this limit problem please help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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El_Arrow
  • El_Arrow
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El_Arrow
  • El_Arrow
i dont understand why she did that
anonymous
  • anonymous
divide top and bottom by \(n^2\) so you can more easily see which terms dominate

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El_Arrow
  • El_Arrow
but if you do that in the bottom for example n^3/n^2 you get n not 1/n
anonymous
  • anonymous
$$\frac{3n^2+2n}{\sqrt{n^3+n^2+1}}\cdot\frac{1/n^2}{1/n^2}=\frac{3n^2+2n}{\sqrt{n^3+n^2+1}}\cdot\frac{1/n^2}{\sqrt{1/n^4}}=\frac{3+2/n}{\sqrt{1/n+1/n^2+1/n^4}}$$ so you can clearly
El_Arrow
  • El_Arrow
oh so you square it when there is a square root?
anonymous
  • anonymous
Actually he did that..
anonymous
  • anonymous
Oh sorry, that was someone else you did that..
anonymous
  • anonymous
see that in the limit as \(n\to\infty\), the square root tends to \(0\) while the top tends to \(3\); this tells us the terms 'blow up' as \(n\) grows larger and larger since the denominator gets ever smaller
anonymous
  • anonymous
\[\sqrt{\frac{1}{x^2}} = \frac{1}{x} = \sqrt{\frac{1}{x^2}}\]
anonymous
  • anonymous
*who..
anonymous
  • anonymous
When you take x inside squares, it becomes \(x^2\)..
anonymous
  • anonymous
*square root brackets..
El_Arrow
  • El_Arrow
oh okay i see
El_Arrow
  • El_Arrow
i have one more question
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El_Arrow
  • El_Arrow
where did the 8 in this problem come from?
anonymous
  • anonymous
the distance between the vertex and focus (\(-4\)) is equal to the distance between the vertex and directrix
El_Arrow
  • El_Arrow
so you are add -4+-4?
anonymous
  • anonymous
|dw:1437367323144:dw|

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