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appleduardo

  • 2 years ago

whats the limit of the following function? could somebody help me pleasE?

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  1. appleduardo
    • 2 years ago
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    \[\frac{ \sqrt{2-t}-\sqrt{2} }{ t }\]

  2. appleduardo
    • 2 years ago
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    t-->0

  3. nasryn
    • 2 years ago
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    first you want to multiply the top and bottom by the reciprocal of the top

  4. nasryn
    • 2 years ago
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    \[\sqrt{2-t}+\sqrt{2}\]

  5. nasryn
    • 2 years ago
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    multiply top and bottom by that, and what do you get?

  6. appleduardo
    • 2 years ago
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    yeep, but then i'll get this: \[\frac{ 2-t-2 }{ t(\sqrt{2-t})+\sqrt{2}}\]

  7. nasryn
    • 2 years ago
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    right.

  8. nasryn
    • 2 years ago
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    now simplify the top

  9. appleduardo
    • 2 years ago
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    ill get:\[\frac{ -t }{ t(\sqrt{2-t} +\sqrt{2}) }\]

  10. nasryn
    • 2 years ago
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    also, the denominator should be \[t(\sqrt{2-t}+\sqrt{2})\]

  11. nasryn
    • 2 years ago
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    correct. now can you do anything with the top and bottom t's?

  12. appleduardo
    • 2 years ago
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    is it right to cancel a negative t with a positive t ?

  13. nasryn
    • 2 years ago
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    well, you just cancel the t's, the negative would stay.

  14. nasryn
    • 2 years ago
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    so you would get \[\frac{ -1 }{ \sqrt{2-t}+\sqrt{2} }\]

  15. nasryn
    • 2 years ago
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    now you can take the limit directly by plugging in 0.

  16. appleduardo
    • 2 years ago
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    :O so the limit is: -0.353509207 ?

  17. nasryn
    • 2 years ago
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    well, I suppose if you want to do it that way, I would just say \[\frac{ -1 }{ 2\sqrt{2} }\]

  18. appleduardo
    • 2 years ago
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    oh God youre a genius! thank you so much!!!

  19. nasryn
    • 2 years ago
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    :) no worries.

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