Consideram [tex] \lim_{x \to 1} \frac{sin( x^{2} -x)}{ x^{2} -1}= \lim_{x \to1} \frac{1}{ \frac{ x^{2} -x+x-1}{sin( x^{2} -x)} }= \lim_{x \to1} \frac{1}{ \frac{( x^{2} -x)}{sin( x^{2} -x)}+ \frac{(x-1)x}{sin( x^{2} -x)}* \frac{1}{x} }= [/tex][tex] \frac{1}{1+1* \frac{1}{1} }= \frac{1}{2}. [/tex]
