# Basic Limit

How do I calculate the limit:
$lim x-> infinity ((2x+1)^13(3x-7)^17)/((3x+5)^30)$

Should I use the binomial theorem to open it up?

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jack action
Gold Member
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I can't use L'Hopital becuase we didn't learn it yet. That's what making this question troubling. The power is 30 in the numerator and the denominator so i'm not sure how to work around it.

Office_Shredder
Staff Emeritus
Gold Member
When taking the limit of a rational function as x goes to infinity you only need to consider the highest degree term in the denominator and the numerator, because the rest of the terms don't grow as fast

Well that's exactly the problem, the denominator and the numerator's power is 30 so it's obviously the same degree. What do I do from this point?

Office_Shredder
Staff Emeritus
Gold Member
If you had to find the limit as x goes to infinity of $$\frac{5x^7}{12x^7}$$, it's obviously 5/12 right? Same deal, find what the coefficient of each term is and that's your limit

jack action