Lim (cos (x) / cos (2x)) ^ (1/x^2)

Question

Алгебра

Дунятка

26 июня, 12:18

Lim (cos (x) / cos (2x)) ^ (1/x^2)

+3

Ответы (1)

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Филипий · Answer 1

Наверно x - > 0

= lim (cos (x) / (1-2sin^2 (x)) ^ (1/x^2) = lim (cos (x)) ^ (1/x^2) = lim (1+cos (x) - 1) ^ (1/x^2) = lim ((1 + [cos (x) - 1]) ^ 1/[cos (x) - 1]) ^ ([cos (x) - 1] / x^2) = e ^ lim (cos (x) - 1) / x^2 = e^-lim (1-cosx) / x^2 = e^-lim [2[sin (x/2) ]^2/[4 * (x/2) ^2] = e^ - 1/2*lim [sin (x/2) / (x/2) ]^2 = e^ - (1/2)