Решите предел. [tex]\lim_{n \to \ 1-0} \frac{|x^{2}-1 |}{sin(x-1)}[/tex]. Created by SeregaAndreev. matematika-ru

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SeregaAndreev @SeregaAndreev

October 2021 1 16 Report

Решите предел.

[tex]\lim_{n \to \ 1-0} \frac{|x^{2}-1 |}{sin(x-1)}[/tex]

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igorShap

Verified answer

$\lim_{x \to 1-0} \frac{|x^{2}-1 |}{sin(x-1)}=[t=1-x]=\lim_{t \to +0} \frac{|(1-t)^{2}-1 |}{sin(-t)}=\lim_{t \to +0} \frac{|t^2-2t |}{-t}=\lim_{t \to +0} \frac{2t-t^2}{-t}=\lim_{t \to +0} -2+t=-2$

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