Question

can't quite figure out the limit problem ​

Answer 1

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.