Infinite Discontinuity
Infinite Discontinuity - Related Videos
07:22
Discontinuing Intravenous Fluids and a Peripheral Intravenous Line
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2023
Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT Intravenous (IV) fluid administration and peripheral IV catheters (PIVs) may be discontinued for a number of reasons. The most common reason for discontinuing IV fluids is that the patient has returned to normal body fluid volume (euvolemia) and is able to maintain adequate oral fluid intake or is being discharged from the hospital. In addition, the Centers for Disease Control Guidelines...
01:28
Introduction to Infinite Series
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2026
An infinite series is the sum of an infinite sequence of terms. Instead of adding only a fixed number of values, the addition continues without end. To make sense of this process, mathematicians examine partial sums, which are running totals formed by adding the first few terms of the series. If these partial sums approach a fixed number, the infinite series is said to converge. If they do not approach a finite value, the series diverges.The water tank example illustrates convergence through...
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Infinitely Repeated Games
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2025
An infinitely repeated game is a scenario where players repeatedly engage in the same game without a predetermined end. This concept is crucial in understanding long-term interactions in various fields of the social sciences, including economics and international relations. Examples: Firms Setting Prices: Companies continuously adjust prices. Trade Negotiations: Countries consistently negotiate trade terms. Tit-for-Tat Strategy Cooperative Start: Players begin with a cooperative action,...
02:17
Separation of Bacteria by Capsule Amount Using a Discontinuous Density Gradient
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2025
Source: Feltwell, T., et.al. Separating Bacteria by Capsule Amount Using a Discontinuous Density Gradient. J. Vis. Exp. (2019)This video demonstrates the use of a discontinuous density gradient to separate bacterial strains based on capsule amount. By centrifuging a transposon mutant library through the gradient, bacteria with different capsule densities localize to distinct layers. The separated fractions can then be collected for downstream analysis.
07:28
A Contusive Model of Unilateral Cervical Spinal Cord Injury Using the Infinite Horizon Impactor
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Cited by 46 •
2012
A reliable and repeatable way to produce a cervical unilateral spinal cord injury using the Infinite Horizon impactor is described. The method takes advantage of a custom designed frame and clamp to stabilize the spine. The standardized procedure and biomechanical injury parameters result in sufficient and sustained injuries.
FAQs
The left-hand and right-hand limits must be examined separately because they can approach positive infinity, negative infinity, or different unbounded behaviors. If only one side grows without bound, the discontinuity is one-sided. If both sides become unbounded, their signs and directions describe the graph near the point and clarify how the function approaches its vertical asymptote.
A vertical asymptote records an input value that the graph approaches while the function’s outputs increase or decrease without bound. The asymptote therefore describes the graph’s structure even though the function does not approach a finite height there. Checking one-sided behavior shows whether the graph rises, falls, or behaves differently on opposite sides.
The distinction depends on the limiting behavior near the input. A removable discontinuity has a finite limit that may be missing from the function, while a jump discontinuity has different finite one-sided limits. Infinite discontinuity instead involves unbounded one-sided or two-sided behavior, so it cannot be repaired by assigning one finite function value at the point.
First locate inputs where the function may fail to remain finite, then inspect the behavior from the left and right. Determine whether either one-sided limit becomes positive or negative infinity. On a graph, look for branches that rise or fall without bound near the same input. That input identifies the relevant vertical asymptote when one is present.
For 1/(x−a), the expression changes behavior at x = a because the denominator becomes zero there. As the input approaches a from either side, the function’s values become unbounded, with the direction depending on the side of approach. This example illustrates how an algebraic expression can reveal both the discontinuity’s location and its vertical graph structure.
An infinite discontinuity can occur at an endpoint or inside the interval of an improper integral, making ordinary finite-area reasoning insufficient. The integral must therefore be considered in relation to the unbounded behavior and the appropriate one-sided approach. Recognizing the discontinuity identifies where the integral requires special analysis rather than routine substitution or direct evaluation.