Finding the limit of rational function as x approaches infinity

[919_is]

Find the limit:


Lim
x --> infinity

4x²+9x
5x²+8



Lim
x --> infinity

(4x²/x²)+(9x/x²)
(5x²/x²)+(8/x²)



Lim
x --> infinity

4+(9/x)
5+(8/x²)


Lim
x --> infinity

4 +04
5 + 0 = 5


1) Did I do this process correct?
2) Why does dividing constant by infinity will result to zero?
3) What if the answer is 4 + infinity instead of 4 + 0 .... will the answer be the same or will it be infinity?



I would appreciate any help. Thanks

 

[biffboy]

limit

As x increases both 9/x and 8/x^2 get smaller and smaller. That is as x-> inf they both -> 0. So your answer is 4/5

 

[HallsofIvy]

3) What if the answer is 4 + infinity instead of 4 + 0 .... will the answer be the same or will it be infinity?

"infinity" is not a number and neither is "4+ infinity" That's why it is better to get things that go to 0.

I would appreciate any help. Thanks