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A differentiable function. In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain.In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain.
Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise. Minkowski's question mark function: Derivatives vanish on the rationals. Weierstrass function: is an example of continuous function that is nowhere differentiable
Early in the history of calculus, many mathematicians assumed that a continuous function was differentiable at most points. [14] Under mild conditions (for example, if the function is a monotone or a Lipschitz function), this is true. However, in 1872, Weierstrass found the first example of a function that is continuous everywhere but ...
It states that if f is continuously differentiable, then around most points, the zero set of f looks like graphs of functions pasted together. The points where this is not true are determined by a condition on the derivative of f. The circle, for instance, can be pasted together from the graphs of the two functions ± √ 1 - x 2.
Special functions: non-elementary functions that have established names and notations due to their importance. Trigonometric functions: relate the angles of a triangle to the lengths of its sides. Nowhere differentiable function called also Weierstrass function: continuous everywhere but not differentiable even at a single point.
differentiable function A differentiable function of one real variable is a function whose derivative exists at each point in its domain. As a result, the graph of a differentiable function must have a (non-vertical) tangent line at each point in its domain, be relatively smooth, and cannot contain any breaks, bends, or cusps. differential ...
The needs of geometry, and also for example classical mechanics are to have a notion of curve in space of any number of dimensions. In general relativity, a world line is a curve in spacetime. If is a differentiable manifold, then we can define the notion of differentiable curve in . This general idea is enough to cover many of the applications ...
The web graph W 4,2 is a cube. The web graph W n,r is a graph consisting of r concentric copies of the cycle graph C n, with corresponding vertices connected by "spokes". Thus W n,1 is the same graph as C n, and W n,2 is a prism. A web graph has also been defined as a prism graph Y n+1, 3, with the edges of the outer cycle removed. [7] [10]