When evaluating limits at infinity or negative infinity, there are a couple methods you can use.  Look at these three examples.


Lim (x --> infinity)  (x^3 + 4x^2 - 3)/(4x^3 + 6x)

You can divide each term by x to the highest power in the problem, which is 3. So divide each term by x^3 to get

Lim (x --> infinity) (1 + 4/x - 3/x^3)/(4 + 6/x^2)

as x tends to infinity, the numerator is just 1 because 4/x and 3/x^3 approach zero. Similarly 6/x^2 approaches zero so the denominator is just 4.  Therefore the limit is 1/4.

Another way to do this problem is that since the highest power of x is the same in both numerator and denominator, divide the coefficients of those two terms which is just 1/4.


If the highest power in the numerator is less than the highest power in the denominator, the lim as x tends to infinity or negative infinity is 0. If the highest power in the numerator is greater than the highest power in the denominator, the lim as x tends to infinity or negative infinity is undefined