lim (t->0) t/(2 * sin^2 (t/6) + 3^(1/2) * sin t/3)) = lim (t->0) 1/(2 * sin^2 (t/6)/t + 3^(1/2) * sin (t/3)/t)
lim (t->0) sin (t/a)/t = | t/a = x, t = ax, t->0 => x ->0 | = lim (x->0) sin x/(ax) = 1/a * lim (x->0) sin x/x = 1/a
Тогда
lim (t->0) 1/(2 * 1/6 * sin (t/6) + 3^(1/2) * 1/3) = 1/(1/3 * 0 + 1/3^(1/2)) = 3^(1/2)