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The number e is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithm function. It is the limit of as n tends to infinity, an expression that arises in the computation of compound interest. It is the value at 1 of the (natural) exponential function, commonly ...
Additional Mathematics. Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school (or GCSE exam takers in the United Kingdom). It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.
PGF. In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a k -sided dice rolled n times. For n independent trials each of which leads to a success for exactly one of k categories, with each category having a given fixed success ...
Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower.
This extended exponential function still satisfies the exponential identity, and is commonly used for defining exponentiation for complex base and exponent. Powers via logarithms. The definition of e x as the exponential function allows defining b x for every positive real numbers b, in terms of exponential and logarithm function.
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe.The inflationary epoch is believed to have lasted from 10 −36 seconds to between 10 −33 and 10 −32 seconds after the Big Bang.
The primary reason for the gamma function's usefulness in such contexts is the prevalence of expressions of the type () which describe processes that decay exponentially in time or space. Integrals of such expressions can occasionally be solved in terms of the gamma function when no elementary solution exists.
For example, let f(x) = 6x 4 − 2x 3 + 5, and suppose we wish to simplify this function, using O notation, to describe its growth rate as x approaches infinity. This function is the sum of three terms: 6x 4, −2x 3, and 5. Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of x ...