If f(x) and g(x) are two functions continuous everywhere and F(x) =
lim {f(x) + x^2n . g(x)}/(1 + x^2n)
n→∞
then prove that F(x) is continuous everywhere except at x = -1, 1. Find the condition on f(x), g(x) which makes F(x) continuous everywhere.
If f(x) and g(x) are two functions continuous everywhere and F(x) =
lim {f(x) + x^2n . g(x)}/(1 + x^2n)
n→∞
then prove that F(x) is continuous everywhere except at x = -1, 1. Find the condition on f(x), g(x) which makes F(x) continuous everywhere.