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1 day ago · This is a consequence of the fundamental theorem of calculus and the fact that the derivative of ln(x) is 1/x. Product and power logarithm formulas can be derived from this definition. For example, the product formula ln(tu) = ln(t) + ln(u) is deduced as:
1 day ago · This definition of exponentiation with negative exponents is the only one that allows extending the identity + = to negative exponents (consider the case =). The same definition applies to invertible elements in a multiplicative monoid , that is, an algebraic structure , with an associative multiplication and a multiplicative identity denoted 1 ...
5 hours ago · An illustration of Newton's method. In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.
1 day ago · Definition The Fourier transform is an analysis process, decomposing a complex-valued function f (x) {\displaystyle \textstyle f(x)} into its constituent frequencies and their amplitudes. The inverse process is synthesis, which recreates f (x) {\displaystyle \textstyle f(x)} from its transform. We can start with an analogy, the Fourier series, which analyzes f (x) {\displaystyle \textstyle f(x ...
5 hours ago · This fact is the basis of a hypothesis test, a "proportion z-test", for the value of p using x/n, the sample proportion and estimator of p, in a common test statistic. For example, suppose one randomly samples n people out of a large population and ask them whether they agree with a certain statement. The proportion of people who agree will of ...
5 hours ago · Meditation is a practice in which an individual uses a technique – such as mindfulness, or focusing the mind on a particular object, thought, or activity – to train attention and awareness, and achieve a mentally clear and emotionally calm and stable state.
1 day ago · Kerényi suggests that Hephaestus may in fact be the "successor" of Prometheus, despite Hephaestus being himself of archaic origin. Pausanias recorded a few other religious sites in Greece devoted to Prometheus. Both Argos and Opous claimed to be Prometheus' final resting place, each erecting a tomb in his honour.
