
#1
Apr509, 01:23 PM

P: 1

Hi all
This is my first post so please be gentle with me! Limit of this rational function as x approaches infinity? f(x) = (x^3  2x)/(2x^2  10) I was under the impression that if the degree of the polynomial of the numerator exceed that of the denominator then there could be no horizontal asymptote. Is this correct? I've used l'hopitals rule and found the limit to be 3x/2. I've been told the limit as x tends to infinity is x/2. Which is the correct solution and why? This has been driving me crazy!! Damian 



#2
Apr509, 01:50 PM

Sci Advisor
HW Helper
P: 3,680

It's x/2. Just divide everything by 2x^2.




#3
Apr509, 01:53 PM

P: 370

Or, just retain the highest order term in the numerator and also in the denominator.
This leaves a ratio of [tex] {{x}\over{2}}[/tex] 



#4
Apr709, 01:12 AM

P: 534

annoyingly simple problem  rational functions and limits at infinity
The limit is [tex]\infty[/tex]. You can find that by taking the above suggestions and taking x/2 as x goes to infinity, but x/2 itself is not the limit.




#5
Apr709, 09:23 AM

P: 370





#6
Apr809, 12:15 AM

P: 534

I'm not misunderstanding anything. The question didn't ask about the asymptotic behaviour of the function as x goes to infinity; it only asked about the limit. I was giving a clear answer to the question.




#7
Apr809, 08:32 AM

P: 370

If you are saying that the wording of the question is vague and that the answer of infinity could be acceptable as an answer, I won't argue about that. 



#8
Apr809, 08:09 PM

P: 534

I didn't find the problem statement unclear or ambiguous at all. Oh well.




#9
Apr809, 09:09 PM

P: 490

The limit of the function as x approaches infinity is undefined (it tends towards infinity).
The f(x)  x/2 goes to zero in the limit of large n, implying that the function f(x) ~ x/2 asymptotically. 



#10
Apr909, 11:24 AM

P: 370





#11
Apr909, 11:55 AM

Sci Advisor
HW Helper
P: 3,680

[tex]\lim_{x\to\infty}f(x)=+\infty.[/tex] If you really want to get technical, what the original poster was asking for is the first term of the asymptotic expansion of f(x) about infinity: [tex]f(x)=\frac x2+\frac{3}{2x}+\frac{15}{2x^3}+\frac{75}{2x^5}+\cdots[/tex] 


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