Posted by Jake on .
Let f(x)=(2x^3x^2+2x+1)/(x^2+1). What is the equation of the oblique asymptote of f(x)?
Can someone show me how to do the long division one for this question. I have always used synthetic division but realized there are some questions that require to do long division.

Calculus 
Steve,
as x gets very large, the higher powers dominate, making the lower powers insignificant. So, for large x,
f(x) looks very much like 2x^3/x^2 = 2x
As x gets bigger and bigger, y gets closer and closer to just 2x.