Question

In the limit `lim 16/x^4=oo` as `x->0`, how do you find `delta>0` such that whenever `0<absx<delta`, `16/x^4>10,000`?

Answer 1

Solve the inequality.

Explanation:

`16/abs(x)^4>10,000` is equivalent to

`16/(10,000) > abs(x)^4`

so

`abs(x) < root(4)(16/(10,000))`
and

`absx < 2/10 = 0.2`

Let `delta = 0.2`