Qohen Leth
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2 days ago · Taking the path (x, y) = (t, 0) → (0, 0), we obtain (,) = =, while taking the path (x, y) = (t, t) → (0, 0), we obtain (,) = + =. Since the two values do not agree, f does not tend to a single value as ( x , y ) approaches (0, 0) .
4 days ago · In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1 2. Many consider it to be the most important unsolved problem in pure mathematics. [1] .
Jun 23, 2024 · The boundary condition \(y(0)=0\) requires that \(c_{1}=0\), so \(y=c_{2}e^{-3x/2}\sin\omega x\), which holds with \(c_{2}\ne0\) if and only if \(\omega=n\pi\), where \(n\) is an integer. We may assume that \(n\) is a positive integer. (Why?).
2 days ago · In particular, when \(p\) is prime, \({\mathbb Z}_p^*\) consists of all the elements of \({\mathbb Z}_p\) except \(0,\) so it has \(p-1\) elements. This is the setup for one of the first nontrivial theorems of elementary number theory, known as Fermat's little theorem. If \(p\) is prime and \(p \nmid a,\) then \(a^{p-1} \equiv 1 \pmod p.\)
4 days ago · Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. Therefore, even at absolute zero, atoms and molecules retain some vibrational motion.
Jun 21, 2024 · The Fundamental Theorem of Calculus, Part 2 (also known as the evaluation theorem) states that if we can find an antiderivative for the integrand, then we can evaluate the definite integral by evaluating the antiderivative at the endpoints of the interval and subtracting.
Jun 13, 2024 · Rational Root Theorem also called Rational Zero Theorem in algebra is a systematic approach of identifying rational solutions to polynomial equations. According to Rational Root Theorem, for a rational number to be a root of the polynomial, the denominator of the fraction must be a factor of the leading coefficient (the coefficient of the term ...
