1. Let f(a) = e^a at x = a and let "a" be rational.
In the neighbour hood of a⁻, let there be an irrational number b = a⁻
f(b) = e^(1-b)
As x (and b) approaches a⁻, its value is e^(1-a⁻)
For the function to be continuous at the point "a",
e^a = e^(1-a⁻) a = 1 - a⁻
as a⁻ approaches, "a", 2a = 1 a = 1/2
The function is continuous only at 1/2. At other values of x in (0,1), the function has different values for a⁻, a and a⁺. SO it is not continuous.
So the series x_n/n converges to the value c.