- #1
shooba
- 9
- 0
When finding the asymptote of a rational function, if the degree of the numerator is less than or equal to the denominator you can divide by the highest power in the denominator and then take the limit as x goes to +/- infinity.
Apparently this trick does not work when the numerator is of higher degree and you are finding the slant asymptote, and you must use long division. I assume this has something to do with the fact that there isn't really a limit because you aren't approaching a number, but it seems like all the terms with x in their denominator should approach 0 and the x-to-the-something term in the numerator should dominate. I guess the terms with x in their denominator do not approach zero at the same "rate", but why is this not a problem when finding the horizontal asymptote?
I am in my first semester of calculus right now, if that limits the discussion somehow.
Apparently this trick does not work when the numerator is of higher degree and you are finding the slant asymptote, and you must use long division. I assume this has something to do with the fact that there isn't really a limit because you aren't approaching a number, but it seems like all the terms with x in their denominator should approach 0 and the x-to-the-something term in the numerator should dominate. I guess the terms with x in their denominator do not approach zero at the same "rate", but why is this not a problem when finding the horizontal asymptote?
I am in my first semester of calculus right now, if that limits the discussion somehow.