If the function continuous at $x = a$ then the function is bounded around a, true or false and why?
I think this is true because we study the continuity at $x = a$ using limit of $f(x)$ at x=a, am I right? and is my justification enough?
2026-04-06 20:07:12.1775506032
If the function continuous at $x = a$ then the function is bounded around a, true or false and why?
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Choose some $\delta>0$ such that $|f(x)-f(a)|<1$ for all $x$ with $|x-a|<\delta$. Then $\sup_{x\in(a-\delta,a+\delta)}|f(x)|\leq |f(a)|+1$.