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appleduardo Group Title

whats the limit of the following function?

  • one year ago
  • one year ago

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  1. appleduardo Group Title
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    \[\frac{ x ^{2}-\sqrt{x} }{ 1-\sqrt{x} }\]

    • one year ago
  2. appleduardo Group Title
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    x-->1

    • one year ago
  3. zordoloom Group Title
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    Do you know how to solve this?

    • one year ago
  4. shubhamsrg Group Title
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    you may try rationalizing, both numerator and denom separately..

    • one year ago
  5. appleduardo Group Title
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    but how can i do that? do first the denomitador and then de numerator or both at the same time?

    • one year ago
  6. shubhamsrg Group Title
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    doesnt matter..

    • one year ago
  7. shubhamsrg Group Title
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    any order you prefer..

    • one year ago
  8. appleduardo Group Title
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    ??

    • one year ago
  9. zordoloom Group Title
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    The limit is -3.

    • one year ago
  10. shubhamsrg Group Title
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    you may rationalize either denom or nume first,,order wont matter..

    • one year ago
  11. sauravshakya Group Title
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    Use L'Hospital Rule

    • one year ago
  12. appleduardo Group Title
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    mm but how? maybe something like this? \[\frac{ x ^{2} +\sqrt{x} }{ x ^{2} +\sqrt{x} }\] multiply the original function times the rationalization of the numerator?

    • one year ago
  13. godfreysown Group Title
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    i get 3x

    • one year ago
  14. appleduardo Group Title
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    yeep, i know the limit, but what i dont, is how to find it

    • one year ago
  15. zordoloom Group Title
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    Just take the derivative of the top, and then take the derivative of the bottom,

    • one year ago
  16. sauravshakya Group Title
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    It is -3

    • one year ago
  17. zordoloom Group Title
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    Then plug in 1 for x and that will give you the limit.

    • one year ago
  18. appleduardo Group Title
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    mm but how can i find the limit without using L'hopital? cos my teacher doesnt allow me to do that yet, he want me to find the limit algebraically

    • one year ago
  19. appleduardo Group Title
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    :/

    • one year ago
  20. zordoloom Group Title
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    Just multiply top and bottom by conjugates then.

    • one year ago
  21. appleduardo Group Title
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    respectively? i mean the numerator conjugate times the original numerator and the denominator conjugate times the original denominator?

    • one year ago
  22. zordoloom Group Title
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    no,

    • one year ago
  23. zordoloom Group Title
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    What you want to do is rationalize one side.

    • one year ago
  24. zordoloom Group Title
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    So, just multiply top and bottom by 1+sqrt(x)

    • one year ago
  25. zordoloom Group Title
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    You should get 1-x for the bottom

    • one year ago
  26. appleduardo Group Title
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    \[\frac{ x ^{2}-\sqrt{x}(1+\sqrt{x}) }{1-x }\] so thts my result after doing what u said :p is it correct?

    • one year ago
  27. Aussie Group Title
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    you would have parenthesis around x^2 and sqrt x

    • one year ago
  28. appleduardo Group Title
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    mm yes so what can i do next?

    • one year ago
  29. Aussie Group Title
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    I am not sure actually you still have on the denominator 1-1 which is still dividing by a zero

    • one year ago
  30. Aussie Group Title
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    your limit does not exist?

    • one year ago
  31. hartnn Group Title
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    \(\huge\frac{ (x ^{2}-\sqrt{x})(1+\sqrt{x}) }{1-x }\times \frac{x^2+\sqrt x}{x^2+\sqrt x}\)

    • one year ago
  32. hartnn Group Title
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    x^4-x = x(x^3-1) = x(x-1)(x^2x+x+1)

    • one year ago
  33. hartnn Group Title
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    put x=1 after cancelling 1-x

    • one year ago
  34. linknissan Group Title
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    divide both num and dem by x^2..

    • one year ago
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