Question

How do you find the horizontal tangent of `y= (4x^2-2) / (x^2)`?

Answer 1

The horizontal tangent is `y=4`

Explanation:

To look for the horizontal tangent, you look the limit of y as x tends to plus or minus infinity.

You take the highest coefficient of the numerator,

`lim_(x->+-oo)y=lim_(x->+-oo)(4x^2)/x^2=4`

Therefore `y=4` is the horizontal tangent.

graph{(y-(4x^2-2)/x^2)(y-4)=0 [-7.9, 7.906, -1.886, 6.016]}