Question

Let a > 0. Prove that the function f : (0, a) −→ R defined by f(x) = x

2
is continuous but
not uniformly continuous on (0, a).

Answer 1

cannot parse your function.

x/2 ?
x^2 ?

In any case, this might be a good place to start.

math.libretexts.org/Bookshelves/Analysis/Introduction_to_Mathematical_Analysis_I_(Lafferriere_Lafferriere_and_Nguyen)/03%3A_Limits_and_Continuity/3.05%3A_Uniform_Continuity