Question

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

Answer 1

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

Answer 2

@Camila1315 can you do it now ?

Answer 3

Yes the limit would be infinity right?

Answer 4

Nope, how did you infinity ?

Answer 5

did you get*

Answer 6

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

Answer 7

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

Answer 8

Oh is it 4?

Answer 9

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

Answer 10

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

Answer 11

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