Search results
Results from the WOW.Com Content Network
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
As there is zero X n+1 or X −1 in (1 + X) n, one might extend the definition beyond the above boundaries to include () = when either k > n or k < 0. This recursive formula then allows the construction of Pascal's triangle , surrounded by white spaces where the zeros, or the trivial coefficients, would be.
In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering, physics and mathematics. Many are integral operators and differential operators.
[1] The approximation can be proven several ways, and is closely related to the binomial theorem . By Bernoulli's inequality , the left-hand side of the approximation is greater than or equal to the right-hand side whenever x > − 1 {\displaystyle x>-1} and α ≥ 1 {\displaystyle \alpha \geq 1} .