is not an indeterminate form.
Given the function I have found, by long division, that there is a slant asymptote, y=3x.
Further, I wanted to find the same result by the classic limit definition.
I ended up in an indeterminate form.The result should had be the same!What's wrong?
I'm afraid you are confused ... the limit as will determine a horizontal asymptote, but not a slant asymptote.
After you do the long division, you get an expression of the form , where is a remainder that tends to 0 as , telling you that the function value approaches the line