Question

How do you prove the statement lim as x approaches 0 for `x^3=0` using the epsilon and delta definition?

Answer 1

Use the fact that if `absx < 1`, then `abs(x^3) < abs x`.

Explanation:

Given `epsilon > 0`, choose `delta = min{1, epsilon}`

Now if `0 < abs(x-0) < delta` then . . .

etc. to show

`abs(x^3-0) < epsilon`.