Find the horizontal limit(s) of the following function: f(x)= (9x^3-8x^2-8x)/(7-8x-7x^3)

Question

Find the horizontal limit(s) of the following function:

 

f(x)= (9x^3-8x^2-8x)/(7-8x-7x^3)

 

I know that one of the horizontal limits is the -9/7, but I'm still missing one and can't find it, please HELPP!!!

Also, please list all steps!!!

Answer 1

The limit you must be finding must be at infinity and you left that out.  Anyway if you look at the numerator and denominator and look at the highest powers of each

 

1.  If powers are equal in both numerator and denominator then the limit is the coefficient of high power numerator/coefficient of highest power denominator. 

 

2.  If power is greater on top than it is on bottom, the limit goes to infinity or negative infinity depending on if the powers are even or odd

 

3.  If power is greater in denominator, the limit goes to 0 because the bottom is increasing much faster than the top...when you have a smal number over a very large number it will go to 0