appleduardo
  • appleduardo
whats the limit of the following function? could somebody help me pleasE?
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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appleduardo
  • appleduardo
\[\frac{ \sqrt{2-t}-\sqrt{2} }{ t }\]
appleduardo
  • appleduardo
t-->0
anonymous
  • anonymous
first you want to multiply the top and bottom by the reciprocal of the top

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anonymous
  • anonymous
\[\sqrt{2-t}+\sqrt{2}\]
anonymous
  • anonymous
multiply top and bottom by that, and what do you get?
appleduardo
  • appleduardo
yeep, but then i'll get this: \[\frac{ 2-t-2 }{ t(\sqrt{2-t})+\sqrt{2}}\]
anonymous
  • anonymous
right.
anonymous
  • anonymous
now simplify the top
appleduardo
  • appleduardo
ill get:\[\frac{ -t }{ t(\sqrt{2-t} +\sqrt{2}) }\]
anonymous
  • anonymous
also, the denominator should be \[t(\sqrt{2-t}+\sqrt{2})\]
anonymous
  • anonymous
correct. now can you do anything with the top and bottom t's?
appleduardo
  • appleduardo
is it right to cancel a negative t with a positive t ?
anonymous
  • anonymous
well, you just cancel the t's, the negative would stay.
anonymous
  • anonymous
so you would get \[\frac{ -1 }{ \sqrt{2-t}+\sqrt{2} }\]
anonymous
  • anonymous
now you can take the limit directly by plugging in 0.
appleduardo
  • appleduardo
:O so the limit is: -0.353509207 ?
anonymous
  • anonymous
well, I suppose if you want to do it that way, I would just say \[\frac{ -1 }{ 2\sqrt{2} }\]
appleduardo
  • appleduardo
oh God youre a genius! thank you so much!!!
anonymous
  • anonymous
:) no worries.

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