$$ \text{Let }f(x)=x ,x\in \mathbb{Q}\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ } \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }=2-x , x \in \mathbb{R}-\mathbb{Q}$$ show that (i) $\lim_{x\to1}f(x) =1$ , (ii)$\lim_{x\to c}f(x) \text {does not exist, if }c\neq 1$
2026-04-04 04:39:00.1775277540
limit of a function which is defined for rational and irrational points on real line explicitly
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