Задача 71197 Задание №4...

63f257933348577249b52495

04.05.2023 08:31:54

Задание №4

5f3ea7e3faf909182968ddd9

04.05.2023 09:23:27

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[m]lim_{x → 4}\frac{arcsin^2(3(x^2-16))}{sin^2(x-4)}(4x-19)=[/m]

[m]=lim_{x → 4}\frac{arcsin^2(3(x^2-16))}{(3(x^2-16))^2}\cdot lim_{x → 4}\frac{(x-4)^2}{sin^2(x-4)}\cdot lim_{x → 4}\frac{(3(x^2-16))^2}{(x-4)^2(4x-19)}=1\cdot 1\cdot lim_{x → 4}\frac{(3(x^2-16))^2}{(x-4)^2(4x-19)}[/m] неопределенность (0/0)


[m]= lim_{x → 4}\frac{(3(x-4)(x+4))^2}{(x-4)^2(4x-19)}=lim_{x → 4}\frac{(3(x+4))^2}{(4x-19)}=\frac{(3(4+4))^2}{(4\cdot 4-19)}=-192[/m]