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June 4th, 2012, 03:24 PM   #1
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As The Limit Goes To Infinity...



taking the conjugate of the numerator seems long, am I missing something?
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June 4th, 2012, 06:23 PM   #2
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Re: As The Limit Goes To Infinity...

We are given:



I would write:



Now we have:



Which is the the indeterminate form 0/0, thus L'H˘pital's rule gives (after simplification):

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June 4th, 2012, 06:56 PM   #3
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Re: As The Limit Goes To Infinity...

Is there a way to solve without L'H˘pital's rule? I am just studying past tests but our teach said we cannot use L'H˘pital's rule but maybe previous years could... Dunno
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June 4th, 2012, 07:57 PM   #4
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Re: As The Limit Goes To Infinity...

Okay, barring the use of our good friend L'H˘pital, we could complete the square under the radicals to get:



Now, we may observe that:

where hence:

thus, we have:

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June 4th, 2012, 08:11 PM   #5
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Re: As The Limit Goes To Infinity...

nice mark I tried completing the square but made a simple mistake! At least I was headed in the right direction.
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