Задача 54751 6.4.118. [m]\lim_{{x \to 0}} \frac{\ln(1...

5f8fac3dc20ac647c5ab5103

21.10.2020 11:05:39

6.4.118. [m]\lim_{{x \to 0}} \frac{\ln(1 + x^2)}{tg^2 8x}[/m]

5f3ea7e3faf909182968ddd9

21.10.2020 16:08:02

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ln(1+x) ∼ x при x → 0 ⇒ ln(1+[b]x^2[/b]) ∼ [b]x^2 [/b] при x → 0

tgx ∼ x при x → 0 ⇒ tg 8x ∼ 8x при x → 0 ⇒ tg^2 8x =tg8x * tg 8x ∼ 8x *8x=64x^2


[m] lim_{x → 0}\frac{ln(1+x^2)}{tg^28x}=lim_{x → 0}\frac{x^2}{64x^2}=\frac{1}{64}[/m]