Question

Найдите лимит. Не используя правило Лопиталя. Даю максимум баллов.

Answer 1

I hope this helps you

Answer 2

$lim(x -> \frac{\pi}{6}) \frac{ { \cos}^{2}(3x) }{1 - \sin(3x) } = | \frac{0}{0} | = | { \cos }^{2} (3x) = 1 - { \sin}^{2} (3x) = (1 - \sin(3x) )(1 + \sin(3x) )| = lim(x -> \frac{\pi}{6}) \frac{(1 - \sin(3x) )(1 + \sin(3x))}{1 - \sin(3x)} = lim(x -> \frac{\pi}{6})(1 + \sin(3x)) = 1 + 1 = 2$