Epsilon-delta definitoon of continuity for $f : x → x^3$

3 Show, using $\epsilon-\delta$ definitoon of continuity, that $f : x ? x^3$ is
a) continuous at each fixed point $x_0 \in \mathbb{R}$,
b) unifonrmly continuous on $[0,a]$.

  • It's hard to read the definition of the function f. Also. the bounty is way too low.

  • To decide what a fair bounty should be, think about the time one may need to spend to write a good solution for your question.

  • How the function f is defined? The definition is missing.

  • Hi Philip, I just changed the definition.

  • Bounty is waaay to low. It should be at least $15.

  • This problem is much more time consuming than you other problem. I suggest raising the bounty.

  • Sorry Philip, really appreciating your help so far, but my budget is quite strict. I do not expect anyone to solve the problem, but I guess it is better to give it a shot sometimes.


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  • Just so you know, I spend about 45 minutes to write this solution. Please offer higher bounties in future, otherwise you may not get a response.

The answer is accepted.