Question

find the oblique asymptotes of f(x) = (9x-x^3)/(x^2-4). Is this oblique asymptote a linear or nonlinear asymptote

Answer 1

the bottom and top exponent differ by only one degree which means that this oblique is linear....

Answer 2

better put... that highest exponents on top and bottom only differ by one degree; so the oblique is a line

Answer 3

Can you explain how I could solve the equation

Answer 4

solve it for the oblique you mean?

Answer 5

yes

Answer 6

long division:

-x
------------
x^2 -4 |-x^3 +9x
x^3 -4
---------
9x -4 <- remainder

the oblique takes the shape of:

9x-4
-x + ------
x^2-4

the left side part goes to zero is x gets large which means that

y = -x+0 or simply

y = -x is the equation of the line for your oblique asymptote

Answer 7

and by left side I mean right side.... Oy!!

Answer 8

Ok, let me study this for a second. thanks

Answer 9

your seconds up :)

Answer 10

as the bottom of a fraction gets very large:

1
-----------------------------
1000000000000000000000000

the value of the fraction get very very very tiny and gets close to zero at the ends.

Answer 11

so anything with an "x" in the bottom gets thrown out and counted for zero

Answer 12

y = -x+0 would mark the end of the equation?