Use the squeeze theorem; if
1 - x ²/4 ≤ u(x) ≤ 1 + x ²/2,
then taking the limit on each part as x approaches 0 gives
1 ≤ lim [x → 0] u(x) ≤ 1
and so the limit of u(x) as x → 0 is simply 1.
