Limits at infinity

Question

i am confused, we should divide the whole fractions by the greatest power right?

Answer 1

You divide each term by the monomial with the highest power

 

 

Ex..

 

 

     3x^2 + 2x^3                        

----------------------  =  &nbsp-   

     4x + 1 + x^3                    &nbsp

 

 

The highest power is 3, so you divide each term by x^3

 

 

 3/x + 2

-----------

 4/x^2 + 1/x^3 + 1

 

 

As x tends to infinity the limit is 2/1 = 2

 

 

 

You can also find the limit with L'Hopital's Rule:

3x^2 + 2x^3                  6x + 6x^2        6 + 12x
---------------------- = ------------- = --------------- = 12/6 = 2
4x + 1 + x^3                4 + 3x^2                6x