Question

When in the horizontal asymptote 0?

Answer 1

when the degree of the polynomial on top is less than the degree of the polynomial on bottom

Answer 2

Example, x2/x

Answer 3

\[\frac{x}{x^2}\]
\[\frac{x/x}{x^2/x}\]
\[\lim_{x->\infty}\ \frac{1}{x}=0\]

Answer 4

that was odd lol

Answer 5

dont we normally divide out the bottom?

Answer 6

\[\frac{x}{x^2}\]
\[\frac{x/x^2}{x^2/x^2}\]
\[\frac{1/x}{1}=\frac{1}{x}\]

Answer 7

gj lol

Answer 8

when \[\lim_{x\to\infty}f(x)=0\]

or
\[\lim_{x\to-\infty}f(x)=0\]

f(x) need not be a rational function

Answer 9

for example
\[\lim_{x\rightarrow\infty}\frac{\sin(x)}{x}\]

Answer 10

nope it doesn't have to be rational