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- To resolve a removable discontinuity, you first determine the limit of the function as it approaches the point of discontinuity. Then, redefine the function at that specific point to match this limit. By doing this, you effectively 'fill in the hole' in the graph, ensuring that the function becomes continuous at that location.
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The removable discontinuity of a graph is a point where it has a hole. A function f(x) is has a removable discontinuity at x = a if its limit exists at x = a but it is not equal to f(a). Learn more about removable discontinuity along with examples.
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 \(a\). - However, \(\lim_{x \to a} f(x)\) exists. A classic example of removable discontinuity can be represented by the function: \[ f(x) = \frac{x^2 - 1}{x - 1} \]
How do you determine removable discontinuity for a function? Recall that a function f (x) is continuous at a if. lim x→a f (x) = f (a), which can be divided into three conditions: C1: lim x→a f (x) exists. C2: f (a) is defined. C3: C1 = C2. A removable discontinuity occurs when C1 is satisfied, but at least one of C2 or C3 is violated.
A removable discontinuity, also known as a removable singularity, is a type of discontinuity that occurs in a function where there is a hole in the graph at a
What are removable discontinuities? Holes Removable discontinuities are a type of discontinuity that occur in a function when there is a hole in the graph at a certain point or points. These points are typically marked by a point where the function appears to be undefined but can be made continuous by assigning a value...
3 days ago · A real-valued univariate function f=f(x) is said to have a removable discontinuity at a point x_0 in its domain provided that both f(x_0) and lim_(x->x_0)f(x)=L<infty (1) exist while f(x_0)!=L.
At a removable discontinuity, the left-hand and right-hand limits are equal but either the function is not defined or not equal to these limits: lim f(x) = lim f(x) =6 f(x0) + x → x 0 x→ x−. 0. Figure 1: A removable discontinuity: the function is continuous everywhere except one point. sin(x)
