Find the horizontal / vertical asymptotes if exist.

Question

If exist find the horizontal asymptote

(sqrt(x²+x+1))+x

And the second one is find the vertical asymptote if exist

(x²-2)/(x⁴-4)

Answer 1

For large positive x, the expression looks like 2x; for large negative x,

there is an horizontal asymptote of 0

In the second one, factor the denominator.

There is a removable discontinuity at x=2 and x =-2.

The as x gets large in either direction the function goes to 0.