Infinite limits

1. Feb 20, 2014

grace77

Problem statement
Find lim x-> infinity

(5x^2-1)/(x^2)

Revelant equations
None
Attempt at a solution
Just wanted to make sure I did this right.

Since the degree of the numerator is equal to the denominator does that mean that the limit is just the numerical coefficient of the leading term in the numerator and denominator so in this case it would be 5?

2. Feb 20, 2014

SteamKing

Staff Emeritus
Seat of the pants says so, but the proper way to show the limit is to split up the rational expression, do the necessary cancellations, and then evaluate the limits of the resulting expressions.

3. Feb 20, 2014

grace77

In this case if you spilt it up you would get 5(infinity)-1/infinity ?

4. Feb 20, 2014

Ray Vickson

No, never. You want the limit of $f(x) = (5 x^2 - 1)/x^2$. This can be written as
$$f(x) = \frac{5 x^2}{x^2} - \frac{1}{x^2}$$
Do you see now what happens?

5. Feb 20, 2014

grace77

Yes I see it now! It would be equal to 5-0=5!