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**charikaar** using the definition: $\displaystyle \forall \epsilon >0, \exists \delta >0, \forall h, \ |h|<\delta \ : |f(a+h)-f(a)|<\epsilon$.

Prove $\displaystyle f(x)$=$\displaystyle x^{1/3}+x$ is continuous at the point a=0.

given epsilon>0, pick delta , then given h with |h|<delta.

$\displaystyle \delta = \mbox{min}\{1, \epsilon^3/8\}$

we have $\displaystyle |f(a+h)-f(a)|=$ $\displaystyle |h^{1/3} + h| \leq |h^{1/3}|+|h|<?=\epsilon$

does this look good? what shall write for $\displaystyle ?$