Math 441 - 6.3 Uniform Convergence and Differentiation

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Lecture from Math 441, Real Analysis, at Shippensburg University. This lesson is based on section 6.3 from Understanding Analysis, by Stephen Abbott.
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What about if the interval is open in the theorem ?

nuwanpriyankara
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in the 3rd example how can you say that the 2nd condition is also satisfies? that is the derivative of the limit is equals to the limit of the derivative

mathswithmunira