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Christos

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

  • 10 months ago
  • 10 months ago

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  1. satellite73
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    the square root grows slower so the limit will be zero

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

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

    • 10 months ago
  4. Christos
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    sqrt((x-3)/x)

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

    • 10 months ago
  6. Christos
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    Yes thats correct

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

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

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

    • 10 months ago
  10. Christos
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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 :(

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

    • 10 months ago
  12. Christos
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    @satellite73

    • 10 months ago
  13. Christos
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    ohh let me try hold on

    • 10 months ago
  14. Christos
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    What do you mean by limit laws?

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

    • 10 months ago
  16. Christos
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    so thats infinity - infinity - infinity = +infinity?

    • 10 months ago
  17. agent0smith
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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.

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

    • 10 months ago
  19. agent0smith
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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

    • 10 months ago
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