Register to reply 
Rational expression limit problem 
Share this thread: 
#1
Oct505, 11:16 PM

P: 61

Sligtly more complex than the average one, I'd assume. How would I go about proving that the limit of of a rational expression consisting of two polynomials of the same degree goes to one and the limit of one where the degree of the bottom is greater than the degree of the top goes to zero. I'd imagine i'd have to use induction, but I've never learned it!
This step is actually a step in a more complicated problem, which I've got for the most part. 


#2
Oct505, 11:25 PM

Sci Advisor
HW Helper
P: 2,586

Limit as x approaches infinity? Consider:
2x/x this is a rational function of two polynomials of the same degree whose limit is never 1 for any x, it is always 2. Also consider: 2(x+1)/x again, it has a limit of 2 as x approaches infinity, but it's limit isn't always 2, for example, it is 4 when x approaches 1. Perhaps you mean when both polynomials also have the same leading coefficient. In that case, the limit as x approaches infinity will be 1. 


#3
Oct605, 08:54 AM

P: 61

yes, sorry, i meant for the case when the polynomials has the same leading coefficient as the variable approaches infinity.



#4
Oct605, 01:35 PM

P: 61

Rational expression limit problem
so can anyone help me prove this? i'm trying to teach myself induction...



Register to reply 
Related Discussions  
Rational Expression  Precalculus Mathematics Homework  2  
Limit of an indeterminate expression  Calculus & Beyond Homework  5  
Integration with a rational expression  Calculus & Beyond Homework  5  
Rational Expression Word Problem  Precalculus Mathematics Homework  1  
Derive the limit of an expression (1+1/n)^n  General Math  5 