vonjd
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 May13 comment Example for finite dimensional analog of integral transforms @MattL.: To be honest with you I don't know because I don't know the Z-transform well enough. But perhaps you could give an example that contains the elements I asked for in my question? May13 asked Example for finite dimensional analog of integral transforms May9 awarded Notable Question Apr28 awarded Nice Question Apr28 revised Intuition for complex eigenvalues edited title Mar9 accepted Intuition and counterexamples for higher-order derivative test Mar8 comment Intuition and counterexamples for higher-order derivative test I was just talking about your example: In our axiomatic system it is not defined at point $0$ because you are dividing by zero there! I am not talking about nature but only about things happening within the realms of pure maths. Yet could you give me a reference for the number of smooth functions and formulas accessible? Thank you again. Mar8 comment Intuition and counterexamples for higher-order derivative test The intuition is appealing - thank you and +1! Considering your example: I disagree: It does not have a minimum at zero - it has literally nothing at zero because it is not defined there, neither are any of its derivatives (see also comments to my question). Mar8 comment Intuition and counterexamples for higher-order derivative test Is it possible to find a counterexample where you don't have a separate case at the extreme value (as with this example at $0$)? This feels a little bit like cheating because the "original function" is not defined at this point. Mar8 comment Intuition and counterexamples for higher-order derivative test Thank you Daniel: $x^{12}$ doesn't answer my question concerning an intuition. Even $x^4$ would work as an example, this is not the problem. Mar8 asked Intuition and counterexamples for higher-order derivative test Feb25 reviewed Approve How do I solve $y'=\frac{y}{x}\frac{x-y}{x+y}$? Feb25 reviewed Approve Integral equation and constant rules Feb25 reviewed Approve Factoring $x$ out of the denominator of a limit Feb25 reviewed Approve How come we ignore constants when finding derivatives? Feb16 reviewed Approve If a function $f$ is continuous in $[a,∞)$ and finite $\lim_{x→+∞}⁡f(x)$ exists, then it's uniformly continuous in $[a,+∞)$. Feb16 reviewed Approve If f: $[0,\infty)\to \mathbb{R}$ is continuous and uniformly continuous in $[k,\infty]$, then it's uniformly continuous in $[0,\infty]$. Jan27 reviewed Approve $n$ balls of $2^{n}-1$ colors, order not significant, how many combinations? Jan26 reviewed Approve Does this function define an inner product? Jan26 reviewed Approve A subgroup has the same number of left and right cosets - Tricks - Fraleigh p. 103 10.32, 35