f(x) is given below. Then lim f(x)/x² =

Explanation

For small x, sin x = x + O(x³), cos x = 1 − x²/2 + O(x⁴), and tan x = x + O(x³). Expanding the determinant with these approximations gives f(x) = x² + O(x⁴). Therefore lim as x → 0 of f(x)/x² = 1.