Evaluating a limit for a rational expression

[calculus 1983]

Evaluate lim f(x) as x tends to infinity for the function by using algebraic manipulations:

f(x) = (5x^6 - 9x + 5x^8 - 3x^2 - 10x^4) / (29x^5 + 7x^5 - x - 3x^2 - 25x^9)

for both the numerator and the denominator you take the number with the highest power therefore ...

lim f(x) = (5x^8) / (-25x^9 )
x -> oo

what do i do from here? thank you.

 

[stapel]

Reduce the fraction.

Eliz.

 

[calculus 1983]

therefore the answer would be ... 1 / -5x = 0

because of one of 4 rules: for example ... 25/x = 0
when you have x/25 = oo; x/-25 = -oo; and 12x^3 / 36x^3 = 12/36 = 1/3

1 is getting closer and closer to 0 and -5x is bigger ..is that correct