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Was (wer) ist smooth functions - definition
FUNCTION HAVING DERIVATIVES OF ANY ORDER
Smooth function; Infinitely often differentiable function; Smooth map; Infinitely differentiable function; Smooth mapping; Smooth functions; Differentiability class; Differentiabillity class; Geometric continuity; Geometrical continuity; C-infinity function; C-infty function; C-k function; C^k function; C infinity; Parametric continuity; C^n; Smoothing Function; Infinitely differentiable; Geometrical Continuity; C0 continuity; C1 continuity; C2 continuity; Ck space; Cinfty function; Ck function; C∞ function; Differentiability classes; Tangential continuity; Tangent continuity; G⁰; G¹; G²; Gⁿ; Smooth approximation; C-infinity; C^k; Smoothness (mathematics); C1 function; Regularity (smoothness)
![Two [[Bézier curve]] segments attached that is only C<sup>0</sup> continuous](https://commons.wikimedia.org/wiki/Special:FilePath/Parametric continuity C0.svg?width=200 "Two [[Bézier curve]] segments attached that is only C<sup>0</sup> continuous")
.svg?width=200 "The function <math>f:\R\to\R</math> with <math>f(x)=x^2\sin\left(\tfrac 1x\right)</math> for <math>x\neq 0</math> and <math>f(0)=0</math> is differentiable. However, this function is not continuously differentiable.")
.svg?width=200 "x}} > 0}}.")
Smoothness
·noun Quality or state of being smooth.
Smooth muscle
![A series of axon-like swellings, called [[varicosities]] from autonomic neurons, loosely form motor units through the smooth muscle.](https://commons.wikimedia.org/wiki/Special:FilePath/1029 Smooth Muscle Motor Units.jpg?width=200 "A series of axon-like swellings, called [[varicosities]] from autonomic neurons, loosely form motor units through the smooth muscle.")
INVOLUNTARY NON-STRIATED MUSCLE
Smooth muscles; Smooth muscle cells; Smooth muscle cell; Muscle, smooth; Myocytes, smooth muscle; Visceral muscles; Single-unit smooth muscle; Non-striated muscle; Unstriped muscle; Leiomyocyte; Single-unit; Smooth muscle fiber; Smooth muscle fibers; Smooth-muscle; Textus muscularis levis; Textus muscularis nonstriatus; Smooth Muscles; Visceral muscle; Smooth muscle tissue; Involuntary smooth muscle; Multiunit smooth muscle
Smooth muscle is an involuntary non-striated muscle, so-called because it has no sarcomeres and therefore no striations (bands or stripes). It is divided into two subgroups, single-unit and multiunit smooth muscle.
Single-unit smooth muscle
INVOLUNTARY NON-STRIATED MUSCLE
Smooth muscles; Smooth muscle cells; Smooth muscle cell; Muscle, smooth; Myocytes, smooth muscle; Visceral muscles; Single-unit smooth muscle; Non-striated muscle; Unstriped muscle; Leiomyocyte; Single-unit; Smooth muscle fiber; Smooth muscle fibers; Smooth-muscle; Textus muscularis levis; Textus muscularis nonstriatus; Smooth Muscles; Visceral muscle; Smooth muscle tissue; Involuntary smooth muscle; Multiunit smooth muscle
Single-unit smooth muscle, or visceral smooth muscle is a type of smooth muscle found in the uterus, gastro-intestinal tract, and the bladder. In SUVSM, a single smooth muscle cell in a bundle is innervated by an autonomic nerve fiber.
Wikipedia
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called differentiability class. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or function).
