Question

Is there a horizontal asymptote in this function?
y = (x+2)/((x−1)(x^2+3))

Answer 1

Best way is to draw your function.

Answer 2

I have it graphed

Answer 3

Just because it appears on the graph that there is a horz. asymptote doesn't mean that it exists.

Answer 4

vertical asymptote where the denominator is zero, namely \(x=1\)

Answer 5

right, got that part.. but the graph looks like it might have a horz. asymptote at y=0

Answer 6

horizontal asymptote is \(y=0\) since the degree of the numerator is smaller than the degree of the denominator

Answer 7

is that a general rule?

Answer 8

degree of numerator is 1, degree of denominator is 3
yes

Answer 9

okay, well then. How do i prove it using limits.. if we take the limit as x->1 it approaches infinity from both sides, but what about the horz. asym.?

Answer 10

I've only ever used limits with vertical asymptotes but I don't really know... I would go with what satellite is saying because i have also heard that general rule.

Answer 11

@satellite73, is there a way to prove it using limits?

Answer 12

it is obvious, but yes, you can
think of what you would get if you replace \(x\) by \(10^6\)

Answer 13

you would have \(10^6\) in the numerator, but you would have \(10^{18}\) in the denoninator

Answer 14

get a number close to zero

Answer 15

sure do

Answer 16

i see.. alrighty thanks.

Answer 17

yw