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4 problems / if u can solve one of them i would really appreciate it /numerical

Re: 4 problems / if u can solve one of them i would really appreciate it /numerical

For problem 1, the proof is obvious by definition. If $\displaystyle f\in C^n(\Omega)$ then $\displaystyle f^\prime, f^{\prime\prime}, \ldots, f^{(n)}$ are all continuous. Let $\displaystyle g = f'$. Now, what are $\displaystyle f^{\prime\prime}, \ldots, f^{(n)}$ in terms of $\displaystyle g$? What does that tell you about $\displaystyle g$'s differentiability class?

I have no ideas for problems 2-4.