How do you find the slant asymptote of (3x^4 + 5x +1)/(1+x^2) using limits?

The rule is:

a= Lim x--infinity f(x)/x
b= Lim x-- infinity (f(x)-ax)

Question

How do you find the slant asymptote of (3x^4 + 5x +1)/(1+x^2) using limits?

The rule is:

a= Lim x-->infinity f(x)/x
b= Lim x--> infinity (f(x)-ax)

dan815 · Answer

what is a slant asymptote

dan815 · Answer

watch http://www.youtube.com/watch?v=--vh9zgZZmQ

anonymous · Answer

How would you do this using limits?

dan815 · Answer

same as the video

anonymous · Answer

But the video only shows how to do this using division, how would I do this using limits (calculus)?

anonymous · Answer

Using the formula? I just can't seem to solve Lim x--> + infinity f(x)/x!

dan815 · Answer

after you divided you say x is approaching infinity and see what term cancels out

dan815 · Answer

also are you sure your equation isnt 
(3x^3**** + 5x +1)/(1+x^2)

dan815 · Answer

because slant aymptotes only occur when the numerators degree is 1 more than the denominator like he mentions in that video

anonymous · Answer

I'm sure that it's 3x^4!

Does it matter if the difference of degree is more than 1?

anonymous · Answer

If so, does this mean it has no slant asymptote?

anonymous · Answer

http://www.wolframalpha.com/input/?i=graph+%283x%5E4%2B5x%2B1%29%2F%281%2Bx%5E2%29 Not really sure if it looks like it has a slant asymptote?