


What is a removable singularity in complex analysis, and how does it relate to the limit of the function?
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what is a removable discontinuity Informational
- Can a piecewise defined function have a removable discontinuity at the point where the definition changes?
- Give an example of a function with two distinct removable discontinuities.
- Consider the function f(x) = (x^2 + 1) / (x^2 + 1) for x ≠ 1 and f(1) = 0. Does it have a removable discontinuity at x = 1?
- Consider a curve defined parametrically. Can it have a "missing point" corresponding to a removable discontinuity?
- Consider a presheaf of functions with removable discontinuities allowed. How does the associated sheaf behave?
- Consider the piecewise function f(x) = { x + 1 if x ≠ 3, k if x = 3 }. What value of k would make the function continuous at x = 3?
- How do removable discontinuities relate to the concept of conformal mappings in complex analysis?
- Consider a path integral where the integrand has a removable singularity along some path. How is this handled?
- In chemistry, can reaction rates or equilibrium constants exhibit removable discontinuities under certain conditions?
- In signal processing, how can filters be designed to handle or compensate for removable discontinuities in the input signal?
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