Understand the problem
- Both the sequences and converge uniformly on .
- Neither nor converges uniformly on .
- converges pointwise but not uniformly on any interval containing the origin
- converges pointwise but not uniformly on any interval containing the origin.
Source of the problem
Start with hints
Now, as in . Consider . Calculate . What can you say about option 4?
Can you comment about ?
It is clear that $latex f_n'(x)$ is not uniformly convergent on any such $ latex I$. So option 4) is correct
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