Question

How do you evaluate `(x^4+5x^3+2x-1)/(7x^3+2x^2+9x+1)` as x approaches infinity?

Answer 1

`oo`

Explanation:

`lim_(x to oo) (x^4+5x^3+2x-1)/(7x^3+2x^2+9x+1)`

`= lim_(x to oo) (1+5/x+2/x^3-1/x^4)/(7/x+2/x^2+9/x^3+1/x^4)`

`= (lim_(x to oo) 1+5/x+2/x^3-1/x^4)/(lim_(x to oo) 7/x+2/x^2+9/x^3+1/x^4)`

`= 1/0 = oo`

you might have seen this anyway before starting as the dominant term is the `x^4` term in the numerator