Question

If the function f(x) = {x²{e^1/x},x ≠ 0, k , x = 0 where {.} denotes fractional part function, is continuous at x = 0, then

(A) k = 1

(B) f(x) is non-derivable at x = 0

(C) f(x) is derivable at x = 0

(D) f(x) is continuous at every point in its domain.

Answer 1

Correct option (C) f(x) is derivable at x = 0

Explanation:

due to {e^1/x}, will be discontinuous at all value of x, where e 1/x becomes an integer.

i.e. at x = log_2e, log_3e,.....etc.