Given that f (x) is continuous, f (0) = 0, LIM (x tends to 0) f (x) / 1-cosx = 2, then at x = 0, f (x) = 0, then (A: not differentiable, B: differentiable and f (x) = 0 C: Take the minimum value D: take the maximum value, which one to choose and why to seek detailed explanation

Given that f (x) is continuous, f (0) = 0, LIM (x tends to 0) f (x) / 1-cosx = 2, then at x = 0, f (x) = 0, then (A: not differentiable, B: differentiable and f (x) = 0 C: Take the minimum value D: take the maximum value, which one to choose and why to seek detailed explanation

Therefore, X → 0lim [f (x) / 1-cosx] is a limit of "0 / 0" type. Considering Robita's law, we take the derivative of the numerator and denominator respectively, and then take the limit of ratio x → 0lim [f '(x) / SiNx] = 2F' (x) = 2sinx, f (x) = - 2cosx + C, C is a constant, and f (0) = 0, C = 2F (x) = 2-2cosx ① ORF