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First, x → ∞ as t → ∞ and the distance from the curve to the x-axis is 1/t which approaches 0 as t → ∞. Therefore, the x-axis is an asymptote of the curve. Also, y → ∞ as t → 0 from the right, and the distance between the curve and the y-axis is t which approaches 0 as t → 0.
In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as a synonym for "logistic function". Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams).
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
Also called Indianite. A mineral from the lime-rich end of the plagioclase group of minerals. Anorthites are usually silicates of calcium and aluminium occurring in some basic igneous rocks, typically those produced by the contact metamorphism of impure calcareous sediments. anticline An arched fold in which the layers usually dip away from the fold axis. Contrast syncline. aphanic Having the ...
The ratio in the definition of the derivative is the slope of the line through two points on the graph of the function , specifically the points (, ()) and (+, (+)). As h {\displaystyle h} is made smaller, these points grow closer together, and the slope of this line approaches the limiting value, the slope of the tangent to the graph of ...
Tracking the change in location of a glacier terminus is a method of monitoring a glacier's movement. The end of the glacier terminus is measured from a fixed position in neighboring bedrock periodically over time. The difference in location of a glacier terminus as measured from this fixed position at different time intervals provides a record ...
Solutions to a slope field are functions drawn as solid curves. A slope field shows the slope of a differential equation at certain vertical and horizontal intervals on the x-y plane, and can be used to determine the approximate tangent slope at a point on a curve, where the curve is some solution to the differential equation.
A statement such as that predicate P is satisfied by arbitrarily large values, can be expressed in more formal notation by ∀x : ∃y ≥ x : P(y). See also frequently. The statement that quantity f(x) depending on x "can be made" arbitrarily large, corresponds to ∀y : ∃x : f(x) ≥ y. arbitrary A shorthand for the universal quantifier. An ...