Exercise 2 Let define the sequence of function on the interv

Exercise 2. Let define the sequence of function on the interval [-1, 1] by 1. Prove that the sequence of functions f, is uniformly convergent to f on the interval [-1, 1]. 2. Check that each function f1, is continuously differentiable whereas the limit f is not differentiable at x = O. Does it contradict the theorem about the differentiability of the limit. Justify your answer.

Solution

the function fn(x) is ifferentiable in the interval [-1,1] amd the function fn(x) is uniformally convergent as its true.

and in the given interval the function is definedand its differntiable

f(x) is uniformally convergent.