This is a Real Analysis question.

1. Let ( fn) be the sequence of functions defined on [0, 5] by fn(ac) = e(n+1)x for n = 1, 2, .... Show directly from the definition (meaning you should not use any theorems we have proved about uniform convergence - theorems from earlier in the book are fine though) that (fn) converges uniformly on [0, 5). The Definition is below:The sequence (fn ) converges uniformly on S to a function f defined on S if for each c > 0 there exists a number N such that Ifn (a) - f(x) N. (1)