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i5hands
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Homework Statement
Let f(x)= {x^2-7x+10, for x^2 ≠ 25
{ A, for x = 5
{ B, for x = -5
Is there a value of A that makes f continuous at x= 5?
Is there a value of B that makes f continuous at x= -5?
i5hands said:Homework Statement
Let f(x)= {x^2-7x+10, for x^2 ≠ 25
{ A, for x = 5
{ B, for x = -5
Is there a value of A that makes f continuous at x= 5?
Is there a value of B that makes f continuous at x= -5?
A removable discontinuity is a type of discontinuity that occurs in a mathematical function when there is a hole or gap in the graph of the function. This means that the function is undefined at a particular point, but it can be made continuous by redefining the function at that point.
A function will have a removable discontinuity if there is a point where the function is undefined but the limit of the function as it approaches that point exists. In other words, there is a gap in the graph, but it can be filled in to make the function continuous at that point.
A removable discontinuity can be caused by a variety of factors, including a simplification or cancellation of terms in the function, or the presence of an asymptote. It can also occur when a function is defined differently at a particular point than it is on either side of that point.
To find the location of a removable discontinuity, you can look for points where the function is undefined but the limit exists. This can be done by graphing the function or by plugging in values on either side of the potential discontinuity to see if the limit is the same.
Yes, a removable discontinuity can be removed by redefining the function at the point where the discontinuity occurs. This can be done by filling in the gap in the graph with a new point or by simplifying the function to remove the discontinuity altogether.