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In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
For example, the derivative of the sine function is written sin ′ (a) = cos(a), meaning that the rate of change of sin(x) at a particular angle x = a is given by the cosine of that angle. All derivatives of circular trigonometric functions can be found from those of sin( x ) and cos( x ) by means of the quotient rule applied to functions such ...
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CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...
The last expression is the logarithmic mean. = ( >) = (>) (the Gaussian integral) = (>) = (, >) (+) = (>)(+ +) = (>)= (>) (see Integral of a Gaussian function
A logarithmically convex function f is a convex function since it is the composite of the increasing convex function and the function , which is by definition convex.However, being logarithmically convex is a strictly stronger property than being convex.
In general, the infinitely iterated exponential , defined as the limit of as n goes to infinity, converges for e −e ≤ x ≤ e 1/e, roughly the interval from 0.066 to 1.44, a result shown by Leonhard Euler. [11]
For exact powers of 2, this equals the binary logarithm, but it differs from the logarithm for other numbers and it gives 2-adic order rather than the logarithm. [ 20 ] [ 21 ] Michael Stifel published Arithmetica integra in Nuremberg in 1544, which contains a table [ 22 ] of integers and powers of 2 that has been considered an early version of ...