Задача 67194 Вычислить предел lim_x – > 0......

6383ac71f17c401607754173

27.11.2022 23:31:06

Вычислить предел lim_x – > 0...

626fab9a354ab65fb2f43abb

28.11.2022 00:00:47

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[m]\lim_{x \to 0} (\frac{cos(x)}{sin^2(x)} - ctg^2(x)) = \lim_{x \to 0} (\frac{cos(x)}{sin^2(x)} - \frac{cos^2(x)}{sin^2(x)}) = \lim_{x \to 0} \frac{cos(x)-cos^2(x)}{sin^2(x)} =[/m]
[m]=\lim_{x \to 0} \frac{cos(x)(1-cos(x))}{1-cos^2(x)} = \lim_{x \to 0} \frac{cos(x)(1-cos(x))}{(1-cos(x))(1+cos(x))} =\lim_{x \to 0} \frac{cos(x)}{1+cos(x)} = \frac{1}{1+1} = \frac{1}{2}[/m]