The pointwise limit of the sequence of real-value function
fn(x) = x - \(\frac{x^n}{n}\), ∀ x ∈ [0, 1] is
1
f(x) = 0, ∀ x
2
f(x) = \(\left\{ \begin{matrix} \ \ \ 0, x = 0 \\\ 1, else \end{matrix}\right.\)
3
\(f(x) =\left\{ \begin{matrix} 0, & x = 0 \\\ 1, &x = 1 \\\ x,& 0 < x < 1 \end{matrix}\right.\)
4
f(x) = 1, ∀ x