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Results tagged with real-analysis
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user 166628
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
3
votes
Accepted
Periodical functions with $f^{(n)} = f$, but $f^{(k)} \neq f$ for $k\in \{1,\ldots,n-1\}$
You are asking for solutions $f$ to the simple differentiable equation $$f^{(n)}=f$$ that make $f$ real-valued for real-values of $f$ and not of lower degree $k$th-derivative-wise. As is well-known, t …
- 1,453
1
vote
Does the definition of limit correspond to the intuitive notion?
The answer to your question is that Yes, it captures the intuitive understanding of $f(x)\to L$ if $x\to x_0$ (except that technically one requires $0<|x-x_0|<\delta$ rather than $|x-x_0|<\delta$ unle …
- 1,453
12
votes
Axiomatic construction of trigonometric functions
Let me make the opening remark that as expressed in the comments, merely the algebraic identities and the specified values at $x=0$ includes wild examples.
However, as written, your monotonicity requi …
- 1,453