When is $ \overline {T(B)}$ compact?

Question

Let $V$ and $W$ be normed linear spaces and let $ T : V \to W$ be a continuous linear operator. Let $B$ be the closed unit ball in $V$ . In which of the following cases is $ \overline {T(B)}$ compact?

• $ V = C^1[0, 1],W = C[0, 1]$ and $T(f) = f$.
• $V = W = l_2$ and $T(x) = (0,x_1,x_2,\ldots)$, where $x = (x_n)\in l_2$.
• $V = W = l_2$ and $T(x) = (x_1, x_2,x_{10}, 0, 0,0,\ldots)$, where $x = (x_n)\in l_2$.

This is a question from a PhD entrance exam,I cant show any work.

I am sorry for that,Can you kindly give some hints