## anonymous one year ago What is the limit as x approaches infinity for f(x)=4x^2+8x/x^3+7x^2-x-9?

1. math&ing001

When calculating limits near infinity we only take in consideration the highest degree term: $\lim_{x \rightarrow \infty} \frac{ 4x ^{2}+8x }{ x ^{3}+7x ^{2}-x-9 }=\lim_{x \rightarrow \infty} \frac{ 4x ^{2}}{ x ^{3}}$

2. math&ing001

@Camila1315 can you do it now ?

3. anonymous

Yes the limit would be infinity right?

4. math&ing001

Nope, how did you infinity ?

5. math&ing001

did you get*

6. anonymous

When I graphed it I saw the when x kept approaching infinity, the y value was coming from infinity.

7. math&ing001

No need to graph it, just go from here $$\lim_{x \rightarrow \infty} \frac{ 4x ^{2} }{ x ^{3} }$$ and simplify.

8. anonymous

Oh is it 4?

9. math&ing001

$\lim_{x \rightarrow \infty} \frac{ 4x ^{2} }{ x ^{3} }=\lim_{x \rightarrow \infty} \frac{ 4 }{ x }$ Do you know the limit of 1/x near infinity ?

10. anonymous

Im so bad with limits I thought the limit there would be infinity

11. math&ing001

O.K here's a graph that shows you how the 1/x function acts near infinity : |dw:1433595410014:dw|

12. anonymous

Oh so you have to look at x when it is approaching infinity?

13. math&ing001

Yeah, that's how you get the limit from the graph. Can you figure out the limit now ?

14. anonymous

Yeah so the limit would be 0

15. math&ing001

Yep !