



Explain the difference between a removable discontinuity and a point where the function is simply undefined.
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what is a removable discontinuity Informational
- Explain why dividing by zero often leads to discontinuities, including removable ones.
- How do removable discontinuities differ from poles or essential singularities in complex analysis?
- Consider the function f(x) = (x^4 - 16) / (x - 2). Identify the removable discontinuity and the value of the continuous extension.
- Explain the difference between a removable discontinuity and a point where the function is simply undefined.
- What is the limit of a function at a removable discontinuity?
- What is the value that should be assigned to h(x) = (x^3 - 8) / (x - 2) at x = 2 to make it continuous?
- What is the difference between a removable discontinuity and an essential discontinuity?
- In computer graphics, how are gaps in geometric shapes sometimes handled mathematically, and is there a connection to removable discontinuities?
- How can L'Hôpital's Rule be used to find the limit at a removable discontinuity and determine the value of the continuous extension?
- Consider the function k(x) = (x - 5) / ((x - 5)(x + 2)). Where is the removable discontinuity?
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