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

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Answer 1 · 2015-10-07T16:00:23

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

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

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

etc. to show

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

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