Question

Решите предел, пожалуйста​

Answer 1

$\displaystyle \lim_{n \to 0}\Big(1-\cos 5n\Big)\cdot {\rm ctg}^23n=\lim_{n \to 0}\Big(1-\cos 5n\Big)\cdot \dfrac{\overbrace{\cos^23n}^{1}}{\sin^23n}=\\ \\ \\ =\lim_{n \to 0}\dfrac{1-\cos 5n}{\sin^23n}=\lim_{n \to 0}\dfrac{2\sin^2\frac{5n}{2}}{\sin^23n}=\lim_{n \to0}\frac{2\cdot \left(\frac{5n}{2}\right)^2}{(3n)^2}=\dfrac{25}{18}$

Answer 2

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