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El_Arrow

  • one year ago

need help with limit problem

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  1. El_Arrow
    • one year ago
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  2. El_Arrow
    • one year ago
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    okay so my question is why is it dividing by n?

  3. El_Arrow
    • one year ago
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    i thought you divided by the value with the largest power

  4. Melodious
    • one year ago
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    guys pls help me out in my question

  5. El_Arrow
    • one year ago
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    @amistre64

  6. El_Arrow
    • one year ago
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    @IrishBoy123

  7. ganeshie8
    • one year ago
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    Next you should be asking why is it dividing by the term with largest power

  8. El_Arrow
    • one year ago
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    i dont understand

  9. ganeshie8
    • one year ago
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    Notice that "n" is indeed the largest power in the denominator, but clearly you're missing the key point, dividing by "n" is not really necessary here

  10. ganeshie8
    • one year ago
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    Look at the expression \[\dfrac{n^3}{n+8}\] what happens to this term as "n" becomes large ? which one grows faster, numerator or denominator ?

  11. El_Arrow
    • one year ago
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    the denominator

  12. ganeshie8
    • one year ago
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    are you saying "n+8" grows faster than "n^3" ?

  13. ganeshie8
    • one year ago
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    plugin n=10, 100 etc and see which one is growing faster

  14. El_Arrow
    • one year ago
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    no i meant the numerator

  15. ganeshie8
    • one year ago
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    Okay what about the value of expression as "n" gets large ?

  16. El_Arrow
    • one year ago
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    it goes to infinity right

  17. ganeshie8
    • one year ago
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    |dw:1436635975751:dw|

  18. ganeshie8
    • one year ago
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    As you can see the function f(x) = x^3/(x+8) is increasing without any bound as x increases, so the corresponding sequence diverges

  19. ganeshie8
    • one year ago
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    They are dividing top and bottom by "n" so that it becomes easy for you to see the same

  20. ganeshie8
    • one year ago
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    \[a_n = \dfrac{n^3}{n+8} = \dfrac{n^2}{1+8/n}\] "plugin" \(n = \infty\), the expression becomes \[ \dfrac{\infty^2}{1+8/\infty} = \dfrac{\infty^2}{1+0} = \infty\]

  21. El_Arrow
    • one year ago
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    i think i understand better now

  22. ganeshie8
    • one year ago
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    In general : For any rational function, \(f(x) = \dfrac{P(x)}{Q(x)}\) , as \(x\to\infty\), we have \(f(x)\to\pm\infty\) if the degree of \(P(x)\) is greater than the degree of \(Q(x)\)

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is replying to Can someone tell me what button the professor is hitting...

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