16. limx→0(1+3 tgx)9x

16. $$lim_{x \to 0} (1+3 tg x)^{9x}$$

$$lim_{x \to 0} (1+3 tg x)^{9x} = lim_{x \to 0} ((1+3 tg x)^{\frac{1}{3tg x}})^{\frac{3 tg x \cdot 9}{1}} = e^{lim_{x \to 0} 27 tg x} = e^{27 lim_{x \to 0} tg x} = e^{27 \cdot 0} = e^0 = 1$$

Ответ: 1