Question 1:
Assume we already know $x(t):[0,2\pi]\to\mathbb{R}$'s Fourier series $x[n]_{n=-\infty}^\infty$. Perform DFT on $x[n]_{n=0}^N$. How is the result connected to $x(t)$? WHY?
Question 2:
Sample the continuous function $f(x)$ on $N$ points: $nT,n=0,\ldots ,N-1$ where $T$ is sampling cycle. Perform DFT on $\{ f(nT) \}_{n=0}^{N-1}$.
Is the result connected to $f(x)$'s continuous Fourier transform?