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December 3rd, 2013, 02:44 AM   #1
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uni level convergence/limit question

I need to be able to explain the solution to the limit:

.

However, I am unable to solve it.
I have tried using l'Hopital's rule but that seems to make it too complicated, and the squeeze theorem makes it too simplified and I can't get to the desired answer which is 1/2 (I eventually looked up the graph in the hope that it would make it easier to solve).

Any help would be great.
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December 3rd, 2013, 11:58 AM   #2
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Re: uni level convergence/limit question

Have you tried hitting the numerator with the Binomial Theorem?
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December 3rd, 2013, 01:34 PM   #3
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Re: uni level convergence/limit question

Quote:
Originally Posted by RedPanda624
I need to be able to explain the solution to the limit:

.

However, I am unable to solve it.
I have tried using l'Hopital's rule but that seems to make it too complicated, and the squeeze theorem makes it too simplified and I can't get to the desired answer which is 1/2 (I eventually looked up the graph in the hope that it would make it easier to solve).

Any help would be great.
Let y = 1/x and look at the problem as y -> 0. You will find it a lot easier (L'Hopital).
Hint: step2 - multiply by y/y, before L'Hopital.
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