What is the Method for Determining Infinity Limits in a Rational Function?

[camboguy]

ok I am confused when x->negative infinity or positive infinity.

for example

lim (5x^3+27)/(20x^2 + 10x + 9)
x-> negative infinty

heres what i think, i want to know if i have the right idea or not.

- so since the top exponent is larger then the denominator the lim DNE and so i plugged in a negative value to test if it is negative or positive infinity so i put in -1 just to test, the thing is i only plunged it into the (5x^3)/(20x^2); I am thinking this is what i do, and then i get a negative value so i am assuming it is negative infinity. that is what the answer is so posed to be, but did i do it how its so posed to be done?

 

[Dick]

Divide top and bottom by x^2 and get rid of stuff that tends to zero.