Question

Let \(X, Y, Z\) be metric spaces. \(f: X \rightarrow Y\) is called uniformly continuous if
\(\forall \epsilon > 0 \quad \exists \delta > 0 \quad \forall x, y \in X : d_{x}(x,y) \leq \delta \Rightarrow d_{Y}(f(x),f(y))\leq \epsilon \)
Show:

b) \(f(x):=x^{2}\) is continuous, but not uniformly continuous on \(\mathbb{R}\)