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Understanding the definition of domain in Complex Analysis
I have a definition in my book which states, "a nonempty open set that is connected is called a domain." I understand what an open set is (a set containin...
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If a graph has a chromatic number $k$, then for any color there is a vertex of that color that has as neighbors all the other colors
Let $G$ a graph and $k= \chi(G)$. Prove that for all $k$-colorings of $G$ and for all colors $i \in \{1,\ldots,k\} $, there exists $u \in V(G)$ of color $...
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Is there a difference between limit and "two-sided limit"?
If we have a function of real-variable, then we can talk about one-sided limits $\lim\limits_{x\to a^+} f(x)$ and $\lim\limits_{x\to a^-} f(x)$ and, of co...
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Find the mass of the disk. - Double Integration Problem - Calculus 3
A disk of radius $5$ cm has density $10$ g/cm$^2$ at its center, density $0$ at its edge, and its density is a linear function of the distance from the ce...
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Derivative of a right triangle's area with respect to its height
I want to find the first derivative of the area of a right triangle as its non-hypotenuse sides change as a function of a third variable. I try it two dif...
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Is constant a polynomial
Is constant number a polynomial? Is $5$ a polynomial? My present understanding is no: $0$ is a polynomial with no degree be defined, But if $5$ is a polyn...
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Formula for cumulative binomial probability
Is there a simple formula for finding a value of a cumulative binomial probability, eg. like the ones put in cumulative binomial probability tables? eg. X...
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What does "fi" stand for?
Call a statement A of a first-order language L logically true in the probabilistic sense if for all probability functions P, P(A) = 1. Where S is a set of...
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Finding rate of change of angle of elevation
Question- From a building of height $48$ m, a man is walking away at a speed of $2$ m/s. Find the rate of change of angle of elevation, when he is at a di...
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Infinitely many primes of the form $4n+3$
I've found at least 3 other posts$^*$ regarding this theorem, but the posts don't address the issues that I have. Below is a proof that for infi...
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