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In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is also an example of a fractal curve .
A classic example of a pathology is the Weierstrass function, a function that is continuous everywhere but differentiable nowhere. [1] The sum of a differentiable function and the Weierstrass function is again continuous but nowhere differentiable; so there are at least as many such functions as differentiable functions.
In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain.If is a function from real numbers to real numbers, then is nowhere continuous if for each point there is some > such that for every >, we can find a point such that | | < and | () |.
is everywhere continuous. However, it is not differentiable at = (but is so everywhere else). Weierstrass's function is also everywhere continuous but nowhere differentiable. The derivative f′(x) of a differentiable function f(x) need not be continuous. If f′(x) is continuous, f(x) is said to be continuously differentiable.
Approximation of the smooth-everywhere, but nowhere-analytic function mentioned here. This partial sum is taken from k = 2 0 to 2 500. A more pathological example is an infinitely differentiable function which is not analytic at any point. It can be constructed by means of a Fourier series as follows. Define for all
Candy canes are a peppermint treat long associated with Christmas. Learn their history, including why they were first made with red and white stripes.
Mocha Mousse has plenty of perks, according to Li. It’s versatile, calming, and warm, making it a great choice for a variety of spaces. But it’s not without its drawbacks.
If you were around in 1997, you simply could not miss it: "MMMBop" was everywhere. The song, off Hanson's debut "Middle of Nowhere," helped sell more than 10 million albums, and knocked the ...