# Questions tagged [limits]

Questions on the evaluation and properties of limits in the sense of analysis and related fields. For limits in the sense of category theory, use (limits-colimits) instead.

28,326 questions
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### Limit counterexample for infinite union

It is well known that if a function has the same limit on finitely many sets, then the limit exists on the union of those sets. (just choose the minimal delta). I am trying to find a counterexample to ...
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### Relation between limit equals to infinite and limit doesn't exist. [on hold]

Can anyone please tell me the relation between limit equals to infinite and limit does not exist?
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### A taylor series for $\lim \limits_{h \to 0} \frac{\zeta'(-2n-h)}{\zeta(-2n-h)}$ [on hold]

Please help and use Big O Notation, thanks. I tried so-far making a Taylor Series for this limit but my solution is not what I seek for.
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### Prove that any bounded sequence may be split up in countably many sequences having the same limit.

Given a bounded sequence $\{x_n\}$ prove that it may be split into countably many sequences having the same limit. The question is stated as above, without any other constraints on the sequence. I'm ...
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### Convergence of unit vector in dir. of $M^{k}*v$ to the principal eigenvector of M when $k\to \infty$ and M is symmetric

It is a standard fact that a square matrix $M$ of dimension $n$ has at most $n$ distinct eigenvalues, each of them a real number, and the sum of their multiplicities is exactly $n$. We will denote ...