Question

Решите предел.

$\lim_{n \to \ 1-0} \frac{|x^{2}-1 |}{sin(x-1)}$

Answer 1

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