Is Tan(x) Locally Lipschitz?

[gaganaut]

Would a trig function like tan \left(x\right) be locally Lipschitz?

How do we know that, if we know that tan \left(x\right) is not continuously differentiable?

 

[quasar987]

tan(x) is continuously differentiable everywhere where it is defined.

And following my geometrical intuition, I would say that it is locally lip****z, and that you would have to try hard to find a function that is continuous but not locally lipschitz!

 

[Landau]

And following my geometrical intuition, I would say (...) you would have to try hard to find a function that is continuous but not locally lipschitz!

Not that hard though, e.g.
[-1,1]\to\mathbb{R}
x\mapsto x^{1/3}
is not Lipschitz on any nhbd of zero.