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This is a question from the inquiry-based note limit

I am sort of surprised that continuity exists but the limit is undefined. I come up with this example not sure if this is what the highlighted takes about.

$$f:[3,7]\cup\{10\}\to\ \mathbb{R}\\x\mapsto x$$

Does this example satisfies the limit at $10$ do not exist but the function is continuous at $10$?

LJNG
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  • why just down-voted? Being nice could just leave an answer YES or NO – LJNG Nov 27 '22 at 02:25
  • The text is talking of continuity at isolated points. This is just for sake of completeness and by definition every function is continuous at isolated points. The analytical concept of continuity is more about continuity at an accumulation point. – Paramanand Singh Nov 27 '22 at 02:28
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    Yes, it's correct. A perhaps less artificial example is the continuous function $f(x)=\sqrt{x^4-x^2}$, for which $x=0$ is an isolated point of the domain. – Hans Lundmark Nov 27 '22 at 06:35

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