Lim (x- 0) (sin7x +sin3x)/x sinx - вопрос №7515887073 от ivanovaanyuta 04.03.2021 12:03

Question

Алгебра: Lim (x- 0) (sin7x +sin3x)/x sinx

ivanovaanyuta · Answer

Получим неопределенность 0/0

Правило Лопиталя
lim x-> 0 (sin7x +sin3x) ' / (x sinx) ' =
= lim x-> 0 (7cos7x + 3cos3x) / (sinx + x*cosx ) =
= (7cos7*0 + 3cos3*0) / (sin0 + 0*cos0 ) = 10/0 = ∞

Lim (x-> 0) (sin7x +sin3x)/x sinx