Question

Is this limit true or false `lim 1/x^2=-oo` as `x->0`?

Answer 1

False.

Explanation:

`lim_(x->0)1/x^2=oo`

Because the denominator is squared it will always be positive, regardless as to whether we approach `0` from the left or right. So:

as `x->0^-` `color(white)(88)1/x^2->oo`

as `x->0^+` `color(white)(88)1/x^2->oo`

`:.`

`lim_(x->0)1/x^2=oo`