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.

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- Apr 25th 2009, 10:30 PMfardeen_genContinuity of function?
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.