Let f_{n} = . Find the pointwise limit of fn. Is the convergence uniform?
If I'm not mistaken, f_{n} 0, For all x in R.
I believe that for this function the convergence is uniform. By letting N> we have,
< < < .
So our choice of N, only depends on epsilon, for all x in R.
Let f_{n} = . Find the pointwise limit of fn. Is the convergence uniform?
Now f_{n} , for all x in R.
In this case however, there is no uniform convergence because:
So our choice of N would imply taking N > . So our choice of N depends on both epsilon and x. Could it be that for a closed interval of the form [a,b] the convergence is uniform?
Thank you