The function can also be written as . From here we see that if and . As for the next part i think that cannot contain
Examine the functions f_n(x) = x^(2n) / (1+x^(2n)) on R for n = 1,2,...
a) calculate the limit function f of the sequence [f_n]
b) Complete the following sentence: If [f_n] converges uniformly on the interval I=[a,b], then I cannot contain the point(s) x=____. Justify your answer, and then show the convergence is uniform on any closed intervals not containing those points.