Question

when is a horizontal asymptote nonexistant?; and how do you find a slant asymptote? with equation: (x^2+3x+2)/(x-2)

Answer 1

Long division: (x^2+3x+2)/(x-2)

Answer 2

\[\lim_{x\rightarrow\infty}\frac{x^2+3x+2}{x-2}=\lim_{x\rightarrow\infty}\frac{x+3+2/x}{1-2/x}=\infty\quad\Rightarrow\quad\]\[\Rightarrow\quad\mbox{horizontal asymptote doesn't exist}\]\[x\rightarrow\infty:\quad\frac{x^2+3x+2}{x-2}=\frac{x^2-2x+5x-10+12}{x-2}=\]\[=\frac{(x-2)(x+5)+12}{x-2}=x+5+\underbrace{\frac{12}{x-2}}_{\rightarrow 0}\]\[\mbox{slant asymptote is }\quad y=x+5\]
http://www.wolframalpha.com/input/?i=asymptote+y%3D%28x%5E2%2B3x%2B2%29%2F%28x-2%29