The limit of ((3x + 1) / (3 + x)) ^ (1 / (x-1)) when x tends to 1

The limit of ((3x + 1) / (3 + x)) ^ (1 / (x-1)) when x tends to 1

Let f (x) = ((3x + 1) / (3 + x)) ^ (1 / (x-1)) ln f (x) = 1 / (x-1) * ln [(3x + 1) / (x + 3)] = 1 / (x-1) * ln [1 + 2 (x-1) / (x + 3)] when X - > 1, 2 (x-1) / (x + 3) - > 0, LN [1 + 2 (x-1) / (x + 3)] 2 (x-1) / (x + 3) LIM (x - > 1) LNF (x) = LIM (x - > 1