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May 27, 2024 · 10 Examples of Discontinuous Development. Walking Milestone: As infants reach the one-year milestone, they often suddenly transform from crawling or scooting to walking. However, this development is discontinuous as it does not occur gradually over time.
A removable discontinuity, also known as a removable singularity or a removable point, appears when a function has a hole or missing point in its graph. The hole can be filled by modifying or redefining the function at that specific point.
What is a Removable Discontinuity Example? A function y = f(x) has a removable discontinuity at x = a when limₓ → ₐ f(x) ≠ f(a). For example, f(x) = (x 2 - 9) / (x - 3). Then limₓ → ₃ f(x) = limₓ → ₃ [(x -3)(x+3)] / (x - 3) = limₓ → ₃ (x + 3) = 3 + 3 = 6.
What is Removable Discontinuity? A removable discontinuity occurs at a point on a function where the function is not defined, yet the limit as we approach that point exists. Mathematically, for a function \(f(x)\) with a removable discontinuity at \(x = a\), we can say: - \(f(a)\) is undefined or does not equal the limit as \(x\) approaches \(a\).
Feb 7, 2024 · Developmental continuity versus discontinuity, also known as continuous development versus staged development, is a debate among developmental psychologists about whether an individual’s development is a continuous, quantitative process or a discontinuous, qualitative process.
It seems that discontinuity in terms of qualitative changes can be best defined by two characteristics: “emergence,” i.e., the irreducibility of a later stage to an earlier; and “gappiness,” i.e., the lack of intermediate stages between earlier and later forms.
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Jan 11, 2023 · Examples of Removable Discontinuities Example 1. Let $f: \R \to \R$ be the real function defined as: $\forall x \in \R: \map f x = \dfrac {x^2 - 1} {x - 1}$ Then $f$ has a removable discontinuity at $x = 1$. In this case the removable discontinuity may be removed by defining $\map f 1$ to equal $2$. Example 2
