a) For each n N consider : R be given by . Show that { } converges in a pointwise fashion to the zero function on . b) Decide whether the convergence in part a is uniform on . please help
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Originally Posted by thaopanda a) For each n N consider : R be given by . Show that { } converges in a pointwise fashion to the zero function on . b) Decide whether the convergence in part a is uniform on . please help a) Well, for all , . One way to see this is that if you use L'Hopital's Rule times, you'll get b) The derivative of is , so the max on occurs at (for all ), and it follows that , which can clearly be made less than any . (Choosing does it.)
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