Problems
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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 $[-10,10]$.
