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One easily sees that those discontinuities are all removable. By the first paragraph, there does not exist a function that is continuous at every rational point, but discontinuous at every irrational point. The indicator function of the rationals, also known as the Dirichlet function, is discontinuous everywhere. These discontinuities are all ...
Contact discontinuities are discontinuities for which the thermal pressure, the magnetic field and the velocity are continuous. Only the mass density and temperature change. Tangential discontinuities are discontinuities for which the total pressure (sum of the thermal and magnetic pressures) is conserved. The normal component of the magnetic ...
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A simple but very useful consequence of L'Hopital's rule is that the derivative of a function cannot have a removable discontinuity. That is, suppose that f is continuous at a , and that f ′ ( x ) {\displaystyle f'(x)} exists for all x in some open interval containing a , except perhaps for x = a {\displaystyle x=a} .
A removable discontinuity occurs when () = (+), also regardless of whether () is defined, and regardless of its value if it is defined (but which does not match that of the two limits). A type II discontinuity occurs when either f ( c − ) {\displaystyle f(c^{-})} or f ( c + ) {\displaystyle f(c^{+})} does not exist (possibly both).
The second term of the right-hand side is the convective rate of change and expresses the contribution of the particle changing position in space (motion). Continuity in the Eulerian description is expressed by the spatial and temporal continuity and continuous differentiability of the flow velocity field.
Seismic tomography studies have shown significant irregularities within the boundary zone and appear to be dominated by the African and Pacific Large low-shear-velocity provinces (LLSVP). [ 1 ] The uppermost section of the outer core is thought to be about 500–1,800 K hotter than the overlying mantle, creating a thermal boundary layer. [ 2 ]
For example, in the classification of discontinuities: in a removable discontinuity, the distance that the value of the function is off by is the oscillation; in a jump discontinuity, the size of the jump is the oscillation (assuming that the value at the point lies between these limits from the two sides);