use the definition of epsilon-delta to proof f(x)=x^3 is continuous
pls help to solve this
To show that $\displaystyle f(x)= x^3$ is continuous at x= a, you must show that
"Given any $\displaystyle \epsilon> 0$, there exist $\displaystyle \delta> 0$ such that if $\displaystyle |x- a|< \delta$ then $\displaystyle |x^3- a^3|< \epsilon$."
It will help to recognize that $\displaystyle |x^3- a^3|= |x- a||x^2+ ax+ a^2|$ so you will need to find an upper bound on $\displaystyle |x^2+ ax+ a^2|$.