Question

In the limit `lim 1/x^3=oo` as `x->0^+`, how do you find `delta>0` such that whenever `0<x<delta`, `1/x^3>1000`?

Answer 1

Solve the inequality.

Explanation:

Throughout this discussion we have `x > 0`

`1/x^3 > 1000` if and only if

`1 > 1000x^3` (for `x > 0`) if and only if

`1/1000 > x^3`

`x < root(3)(1/1000)`

`x < 1/10`

Let `delta = 1/10` (or any positive number less than or equal to `1/10`)