[tex]\it 2^{log_2 x}=x\\ \\ \\ \lim \limits_{x\ \nearrow1} f(x)=\lim \limits_{x\ \nearrow1} \dfrac{x^2-x}{x-1}=\lim \limits_{x\ \nearrow1}\dfrac{x(x-1)}{x-1}=\lim \limits_{x\ \nearrow1} x=1 \\ \\ \\ \lim \limits_{x\ \searrow1} f(x)=\lim \limits_{x\ \searrow1} 2sin\dfrac{\pi x}{6}=2sin\dfrac{\pi}{6}=2\cdot\dfrac{1}{2}=1\\ \\ \\ Deci,\ \ \lim \limits_{x\ \rightarrow1} f(x)= 1[/tex]
