If is the number of solutions of

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

\alpha

is the number of solutions of

|x|=\log(x-[x])

, where

[\cdot]

denotes the greatest integer function, and

\lim_{x\to\alpha}\frac{xe^{ax}-b\sin x}{x^3}

is finite, find

a-b