Question

How do you find the limit of `(x+x^3-x^5)/(1-x^2-x^4)` as x approaches infinity?

Answer 1

`oo`

Explanation:

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

`=lim_(x to oo) x(1+x^2-x^4)/(1-x^2-x^4)`

`=lim_(x to oo) x(1/x^4+1/x^2-1)/(1/x^4-1/x^2-1)`

..... and as `= lim_(x to oo) 1/x^n = 0, n > 0`

this has a slant asymptote `y = x`

`therefore L = lim_{x to oo} x = oo`