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Prove that if $f(x)$ is continuous on the closed interval $[a,b]$ , then $f(x)$ is uniformly continuous on $[a,b]$ .
Prove that $f(x)=x^2$ is not uniformly continuous on the entire $x$ -axis.
Prove that if $f(x)$ is uniformly continuous on a set $U$ and $a$ is inside $U$ , then $f(x)$ is continuous at $a$ .
Prove that $f(x)=mx+b$ is uniformly continuous on the entire $x$ -axis.
Prove that $f(x)=1/x$ is uniformly continuous on the interval $[1,\infty)$ .
Prove that $x^2$ is uniformly continuous on the domain $[-10,10]$ .