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The ramp function is a unary real function, whose graph is shaped like a ramp. It can be expressed by numerous definitions, for example "0 for negative inputs, output equals input for non-negative inputs". The term "ramp" can also be used for other functions obtained by scaling and shifting, and the function in this article is the unit ramp ...
The above example simply states that the function takes the value () for all x values larger than a. With this, all the forces acting on a beam can be added, with their respective points of action being the value of a. A particular case is the unit step function,
Date/Time Thumbnail Dimensions User Comment; current: 05:14, 2 July 2008: 600 × 340 (1 KB): Qef {{Information |Description={{en|1=Graph of the 'ramp function', from x=-3 to x=+3, with guidelines to illustrate that x=y for x>=0.}} |Source=Own work by uploader, hand-written SVG. |Author=Qef |Date=2008-07-02 |Permission= |other_versions=An
The curve is given by the following parametric equations: [2] ... In 2006, two mathematicians using Mathematica analyzed the function, ...
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning. [ 4 ] The function depends on three parameters, the input x , the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
The Lebesgue criterion for integrability states that a bounded function is Riemann integrable if and only if the set of all discontinuities has measure zero. [5] Every countable subset of the real numbers - such as the rational numbers - has measure zero, so the above discussion shows that Thomae's function is Riemann integrable on any interval.
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4. The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1. The minimum value of x is ...