For each natural number n and each number x in (-1,1), define f_n(x)=sqrt((x^2)+(1/n)) and define f(x)=|x|. Prove that the sequence {f_n} converges uniformly on the open interval (-1,1) to the...

For each natural number n and each number x in (-1,1), define

f_n(x)=sqrt((x^2)+(1/n))

and define f(x)=|x|. Prove that the sequence {f_n} converges uniformly on the open interval (-1,1) to the function f. Check that each function f_n is continuously differentiable, whereas the limit function f is not differentiable at x=0.