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Christos

  • 2 years ago

Solve the limit limit(x-->+infinity) sqrt((x-3)/x)

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  1. satellite73
    • 2 years ago
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    the square root grows slower so the limit will be zero

  2. agent0smith
    • 2 years ago
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    Divide both numerator and denominator by x, to solve it algebraically.

  3. Christos
    • 2 years ago
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    I am sorry the actual epression is sort(x-3/x)

  4. Christos
    • 2 years ago
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    sqrt((x-3)/x)

  5. satellite73
    • 2 years ago
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    \[\lim_{x\to \infty}\sqrt{\frac{x-3}{x}}\]?

  6. Christos
    • 2 years ago
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    Yes thats correct

  7. satellite73
    • 2 years ago
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    then it is one since \(x-3\) and \(x\) grow at the same rate

  8. satellite73
    • 2 years ago
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    think what it would be like if \(x\) was \(1,000\) you would have \[\sqrt{.993}\]

  9. agent0smith
    • 2 years ago
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    \[\Large \lim_{x\to \infty}\sqrt{\frac{x-3}{x}} = \sqrt {\lim_{x\to \infty}\frac{x-3} {x}}\]

  10. Christos
    • 2 years ago
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    bro I am trying to solve this limit actually http://screencast.com/t/Yoo5IO0bRPjD And I ended up in the expression above, but what you give me isnt the final answer, something must be wrong :(

  11. agent0smith
    • 2 years ago
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    @Christos that's a completely different expression... break it up using limit laws.

  12. Christos
    • 2 years ago
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    @satellite73

  13. Christos
    • 2 years ago
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    ohh let me try hold on

  14. Christos
    • 2 years ago
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    What do you mean by limit laws?

  15. agent0smith
    • 2 years ago
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    \[\Large = \lim_{x \rightarrow \infty} \sqrt{x^2 - 3x} -\lim_{x \rightarrow \infty} x\]

  16. Christos
    • 2 years ago
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    so thats infinity - infinity - infinity = +infinity?

  17. agent0smith
    • 2 years ago
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    From a graph it looks like it'll be -1.5, I'm just trying to find a way to show that algebraically.

  18. Christos
    • 2 years ago
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    It's ok man dont brother I found it thank you

  19. agent0smith
    • 2 years ago
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    Yeah i'm glad i didn't try to do it myself... wolfram gives a looooong solution: http://www3.wolframalpha.com/Calculate/MSP/MSP35891gdgbb0f2cc1ecie00005387i303c364idgg?MSPStoreType=image/png&s=42&w=433&h=1816

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