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Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
Tafel plot for an anodic process (). The Tafel equation is an equation in electrochemical kinetics relating the rate of an electrochemical reaction to the overpotential. [1] The Tafel equation was first deduced experimentally and was later shown to have a theoretical justification.
A complete handout about the Lorenz curve including various applications, including an Excel spreadsheet graphing Lorenz curves and calculating Gini coefficients as well as coefficients of variation. LORENZ 3.0 is a Mathematica notebook which draw sample Lorenz curves and calculates Gini coefficients and Lorenz asymmetry coefficients from data ...
The knee of a curve can be defined as a vertex of the graph. This corresponds with the graphical intuition (it is where the curvature has a maximum), but depends on the choice of scale. The term "knee" as applied to curves dates at least to the 1910s, [1] and is found more commonly by the 1940s, [2] being common enough to draw criticism.
Example decision curve analysis graph with two predictors. A decision curve analysis graph is drawn by plotting threshold probability on the horizontal axis and net benefit on the vertical axis, illustrating the trade-offs between benefit (true positives) and harm (false positives) as the threshold probability (preference) is varied across a range of reasonable threshold probabilities.
In figure 3, the income–consumption curve bends back on itself as with an increase income, the consumer demands more of X 2 and less of X 1. [3] The income–consumption curve in this case is negatively sloped and the income elasticity of demand will be negative. [4] Also the price effect for X 2 is positive, while it is negative for X 1. [3]
In CAD area this is a drawback, because CAD systems use polynomials or rational curves. In order to get at least rational curves, the square root of the representation of the parallel curve has to be solvable. Such curves are called pythagorean hodograph curves and were investigated by R.T. Farouki. [14]
The following are usually easy to carry out and give important clues as to the shape of a curve: Determine the x and y intercepts of the curve. The x intercepts are found by setting y equal to 0 in the equation of the curve and solving for x. Similarly, the y intercepts are found by setting x equal to 0 in the equation of the curve and solving ...