Question

In the limit `lim x^-2=oo` as `x->0`, how do you find `delta>0` such that whenever `0<absx<delta`, `x^-2>10,000`?

Answer 1

Please see below.

Explanation:

We want `delta` so that `0 < x < delta` implies `x^-2 > 10,000`.

(Note that `0 < x` makes the absolute value superfluous.)

Solve `delta ^-2 > 10,000`

`100 > delta`, so if `0 < x < delta` then

`1/x^2 > 1/ delta^2 > 10,000`