# Tagged Questions

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How can I create "switches" [the term may be new, but I'll explain it] for piecewise defined functions ? Suppose a function: $$f(x)=\begin{cases}\alpha\;,x\in D_1\\\beta\;,x\in ... 3answers 67 views ### Find a function that is surjective and not injective Rules: No piecewise functions. The function must be even, odd, or both even and odd. It cannot be neither. If this is impossible, prove why. This is just something I came up with for fun while ... 2answers 131 views ### How can I get a good estimation of the following function The function is$$ f(n) = \sum_{i=1}^{n} \frac{1}{2i-1}$$How can I compute for example f(20) or f(50) without using a calculator. I want to have an approximation 1answer 39 views ### Characterization of nowhere differentiable functions Let N:=\{f\in C([0,1])\vert \text{ f is nowhere differentiable } \} and A_n = \{f\in C([0,1]) \vert \exists x\in [0,1]s.t. \forall y\in[0,1]: |f(x)-f(y)|\leq n |x-y|\}. Now I have already ... 1answer 74 views ### Functions which satisfy \mathrm{f}(wz) =w\,\mathrm{f}(z)+z\,\mathrm{f}(w) Let \mathrm{f} be a complex-valued function with the following property:$$\mathrm{f}(wz) =w\,\mathrm{f}(z)+z\,\mathrm{f}(w) $$for all w,z \in \mathbb C. Necessary conditions are that ... 2answers 80 views ### A non-trivial, non-negative, function bounded below by its derivative with f(0)=0? I did not know what to search to see if this existed elsewhere. But, I could not find it. Here's the question, does there exist a continuously differentiable function, f: [0,1] \rightarrow ... 2answers 92 views ### function with restrictions in finding solutions Please help... How to prove the following functional equation, which has no solution. A + B + C + (A + B)C - 2 = 0 has no solution, where A = f(x), B = g(x) and C = h(x). Here A, B and C ... 0answers 269 views ### Can  262537412640768743.99999999999925  be beaten with simple expressions? [closed] We know:$$\begin{align}e^{\pi \sqrt{163}} &= 262537412640768743.9999999999992500726\dots\\ x^{24} - 24&=262537412640768743.9999999999992511239\dots\end{align}$$where x is the real solution ... 2answers 86 views ### Number theory Exercise for positive integer n, how can we show$$ \sum_{d | n} \mu(d) d(d) = (-1)^{\omega(n)}  where $d(n)$ is number of positive divisors of $n$ and $mu(n)$ is $(-1)^{\omega(n)}$ if $n$ is square ...
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The previous question. My goal is to find a function of the difference (error) between F and G generally. F = $\Pi_{0}^{n-1}\frac{365-b}{365}$ G = $\frac {364}{365}^{\frac {n^2-n}{2}}$ Now F ...