Question

How do you find the vertical, horizontal or slant asymptotes for `m(x) = (1-x^2)/(x^3)`?

Answer 1

Horizontal: `larr y = 0 rarr`.

Vertical: `uarr x = 0 darr`.

Explanation:

As `x to +-oo, y to 0`. So, y = 0 is an asymptote.

As `x to 0, y to +_oo`. So, x = 0 is the other asymptote.

There is no quotient in the division #y=(1-x^2)/x^3. So, there is no

slant asymptote.

Interestingly, the horizontal asymptote

y = 0 cuts the graph at `x = +-1`.

graph{yx^3-1+x^2=0 [-10, 10, -5, 5]}