The series expansions are,
tan(x) = x + x^3/3 + 2x^5/15 + 17x^7/315 + ...
sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...
tan(x) - sin(x) = x^3(1/3 + 1/3!) + x^5(2/15 + 1/5!) + x^7(17/315 + 1/7!) + ...
f(x) = [tan(x) - sin(x)]/x^3 = 1/2 + 17x^2/120 + 13x^4/240 + ...
Lim of f(x) as x tends to zero is: 1/2