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October 29th, 2012, 12:28 PM   #1
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Calculus, limits, four problems

Hello to everyone! I have four problem I can't solve.
Please, help me. Thanks a lot beforehand
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October 29th, 2012, 12:34 PM   #2
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Re: Calculus, limits, four problems

First, are you "allowed" to use L'H˘pital's rule?
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October 29th, 2012, 12:57 PM   #3
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Re: Calculus, limits, four problems

I don't know about L'H˘pital's rule yet. I just have started to learn calculus. For examples of solutions I try to insight in understanding of limits. So, I ask of you to solve this limits and try to explain me how you do it.
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October 29th, 2012, 01:07 PM   #4
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Re: Calculus, limits, four problems

Okay, I just wanted to know first before working solutions, only to be told afterwards that L'H˘pital's rule is not allowed. It happens quite a bit with these types of limits.
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October 29th, 2012, 11:50 PM   #5
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Re: Calculus, limits, four problems

I'll work the first one:

1.)

I would break this up into two limits:



Here, the degree in the denominator is greater than that of the numerator, hence:







The degree in the numerator and denominator is the same, so we take the ratio of the leading coefficients:



And so we have:

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October 30th, 2012, 03:47 AM   #6
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Re: Calculus, limits, four problems

If you mean by tg(x) tan(x) then the third and fourth one can be solved by multiplying and dividing by the conjugate.
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October 30th, 2012, 07:42 AM   #7
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Re: Calculus, limits, four problems

Hello, The Crisp!

I'll do the last one . . .


Quote:

Multiply numerator and denominator by the conjugate:

[color=beige]. . [/color]


Divide numerator and denominator by

[color=beige]. . [/color]


Therefore:[color=beige] .[/color]

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October 30th, 2012, 09:08 AM   #8
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Re: Calculus, limits, four problems

Thanks to everyone for answers! I try to solve problem#12. Please, check it !

Problem#12
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October 30th, 2012, 09:10 AM   #9
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Re: Calculus, limits, four problems

P.S. Sorry, Iforgot to rotate the picture
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October 31st, 2012, 11:16 AM   #10
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Re: Calculus, limits, four problems

Quote:
Originally Posted by The Crisp
P.S. Sorry, Iforgot to rotate the picture
I think you have got the idea.
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