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



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appleduardo
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\[\frac{ \sqrt{2t}\sqrt{2} }{ t }\]

appleduardo
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t>0

nasryn
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first you want to multiply the top and bottom by the reciprocal of the top

nasryn
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\[\sqrt{2t}+\sqrt{2}\]

nasryn
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multiply top and bottom by that, and what do you get?

appleduardo
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yeep, but then i'll get this: \[\frac{ 2t2 }{ t(\sqrt{2t})+\sqrt{2}}\]

nasryn
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right.

nasryn
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now simplify the top

appleduardo
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ill get:\[\frac{ t }{ t(\sqrt{2t} +\sqrt{2}) }\]

nasryn
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also, the denominator should be \[t(\sqrt{2t}+\sqrt{2})\]

nasryn
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correct. now can you do anything with the top and bottom t's?

appleduardo
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is it right to cancel a negative t with a positive t ?

nasryn
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well, you just cancel the t's, the negative would stay.

nasryn
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so you would get \[\frac{ 1 }{ \sqrt{2t}+\sqrt{2} }\]

nasryn
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now you can take the limit directly by plugging in 0.

appleduardo
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:O so the limit is: 0.353509207 ?

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

appleduardo
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oh God youre a genius! thank you so much!!!

nasryn
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:) no worries.