
cortex
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math question
#11401466  11/07/09 12:48 AM (8 years, 9 months ago) 


i know this should be easy, but i am having trouble showing this:
let P(x) and Q(x) be polynomials.
find the limit as x>infinity of P(x)/Q(x) if the degree of P(x) is 2 and the degree if Q(x) is 7
i have a big math test coming up and i have a practice test with tons of problems, so expect me to ask more questions after i get help with this one.
thanks

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frith
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Re: math question [Re: cortex]
#11401506  11/07/09 12:56 AM (8 years, 9 months ago) 


42


DieCommie
Registered: 12/11/03
Posts: 29,258

Re: math question [Re: frith]
#11401573  11/07/09 01:07 AM (8 years, 9 months ago) 


The quick and easy way is to look at the ratio of leading coefficients. The leading coefficients are the coefficients of your highest power. In your case that is 7. Now the coefficient of P's seventh power of x is '0'. The coefficient of Q's is some number, 'N'. The ratio is 0/N also known as 0.
A more thoughtful way is to consider L'Hospital's rule. Here you get an indeterminate form where both top and bottom separately to to infinity. So you can take the derivative of the top and bottom separately (dont use the quotient rule) and then try a limit. Again you will get an indeterminate form. You can continue taking derivatives an limits until you reach an answer that is not an indeterminate form. In this case that would require 7 derivatives and would give you 0/N.

cortex
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ah, nice, thanks, i should have known it would involve L'Hospital's rule, since that was a big thing we covered a couple weeks ago!

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cortex
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Re: math question [Re: cortex]
#11401695  11/07/09 01:25 AM (8 years, 9 months ago) 


okay, i got another one, i'm not quite sure where to start:
The area of the region that lies to the right of the yaxis and to the left of the parabola is given by the integral . Find the area under the region.
Again, I know I know this, just where do I start? Do I just evaluate that integral at the end points?

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HighTek
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Re: math question [Re: cortex]
#11405545  11/07/09 05:00 PM (8 years, 9 months ago) 


Its a straight forward integration problem evaluated from 0 to 5.
Edited by HighTek (11/07/09 05:00 PM)

cortex
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Posts: 15,167
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Re: math question [Re: HighTek]
#11405550  11/07/09 05:01 PM (8 years, 9 months ago) 


thanks that's what i thought, the wording of the question just made me unsure

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HighTek
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Re: math question [Re: cortex]
#11405576  11/07/09 05:06 PM (8 years, 9 months ago) 


Yeah, I had to read it twice to make sure. Drawing it usually helps.

