# Math Help - y=x^3 (continuity)

1. ## y=x^3 (continuity)

use the definition of epsilon-delta to proof f(x)=x^3 is continuous
pls help to solve this

2. Originally Posted by chelloveck
use the definition of epsilon-delta to proof f(x)=x^3 is continuous
pls help to solve this
To show that $f(x)= x^3$ is continuous at x= a, you must show that
"Given any $\epsilon> 0$, there exist $\delta> 0$ such that if $|x- a|< \delta$ then $|x^3- a^3|< \epsilon$."

It will help to recognize that $|x^3- a^3|= |x- a||x^2+ ax+ a^2|$ so you will need to find an upper bound on $|x^2+ ax+ a^2|$.

3. If you're still stuck, observe that if $|x-a| < 1$, then $|x| < 1 + |a|$ and then follow from that.