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appleduardo

  • 3 years ago

whats the limit of the following function?

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  1. appleduardo
    • 3 years ago
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    \[\frac{ x ^{2}-\sqrt{x} }{ 1-\sqrt{x} }\]

  2. appleduardo
    • 3 years ago
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    x-->1

  3. zordoloom
    • 3 years ago
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    Do you know how to solve this?

  4. shubhamsrg
    • 3 years ago
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    you may try rationalizing, both numerator and denom separately..

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

  6. shubhamsrg
    • 3 years ago
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    doesnt matter..

  7. shubhamsrg
    • 3 years ago
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    any order you prefer..

  8. appleduardo
    • 3 years ago
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    ??

  9. zordoloom
    • 3 years ago
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    The limit is -3.

  10. shubhamsrg
    • 3 years ago
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    you may rationalize either denom or nume first,,order wont matter..

  11. sauravshakya
    • 3 years ago
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    Use L'Hospital Rule

  12. appleduardo
    • 3 years ago
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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?

  13. godfreysown
    • 3 years ago
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    i get 3x

  14. appleduardo
    • 3 years ago
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    yeep, i know the limit, but what i dont, is how to find it

  15. zordoloom
    • 3 years ago
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    Just take the derivative of the top, and then take the derivative of the bottom,

  16. sauravshakya
    • 3 years ago
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    It is -3

  17. zordoloom
    • 3 years ago
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    Then plug in 1 for x and that will give you the limit.

  18. appleduardo
    • 3 years ago
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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

  19. appleduardo
    • 3 years ago
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    :/

  20. zordoloom
    • 3 years ago
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    Just multiply top and bottom by conjugates then.

  21. appleduardo
    • 3 years ago
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    respectively? i mean the numerator conjugate times the original numerator and the denominator conjugate times the original denominator?

  22. zordoloom
    • 3 years ago
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    no,

  23. zordoloom
    • 3 years ago
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    What you want to do is rationalize one side.

  24. zordoloom
    • 3 years ago
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    So, just multiply top and bottom by 1+sqrt(x)

  25. zordoloom
    • 3 years ago
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    You should get 1-x for the bottom

  26. appleduardo
    • 3 years ago
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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?

  27. Aussie
    • 3 years ago
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    you would have parenthesis around x^2 and sqrt x

  28. appleduardo
    • 3 years ago
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    mm yes so what can i do next?

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

  30. Aussie
    • 3 years ago
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    your limit does not exist?

  31. hartnn
    • 3 years ago
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    \(\huge\frac{ (x ^{2}-\sqrt{x})(1+\sqrt{x}) }{1-x }\times \frac{x^2+\sqrt x}{x^2+\sqrt x}\)

  32. hartnn
    • 3 years ago
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    x^4-x = x(x^3-1) = x(x-1)(x^2x+x+1)

  33. hartnn
    • 3 years ago
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    put x=1 after cancelling 1-x

  34. linknissan
    • 3 years ago
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    divide both num and dem by x^2..

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