Limit

 $\lim_{x\rightarrow1}\left(\frac{1}{x-1}-\frac{2}{x^2-1}\right)=\ ?$  

 $If\ \ \lim_{x\rightarrow2}\ \frac{\left(x^n-2^n\right)}{\left(x-2\right)}\ \ =\ 12,\ then\ find\ n.$  

 $\lim_{x\rightarrow0}\ \frac{\left(2^{3x}-3^x\right)}{\sin5x}\ =?$  

 $\lim_{x\rightarrow0}\ \frac{\left(8^x-4^x-2^x+1\right)}{x^2}=?$  

 $\lim_{x\rightarrow-1}\ \frac{\left(x+1\right)}{x^3+1}=\ ?$  

 $\lim_{x\rightarrow0}\ \ \frac{\left(1+x\right)^{\frac{1}{3}}-\left(1-x\right)^{\frac{1}{3}}}{\sqrt{1+x}-\sqrt{1-x}}\ =\ ?$  

 $\lim_{x\rightarrow\infty}\left\{\sqrt{x+1}-\sqrt{x}\right\}=?$  

 $\lim_{n\rightarrow\infty}\ \ \frac{\left(1+\frac{1}{2}+\frac{1}{2^2}+.......+\frac{1}{2^n}\right)}{\left(1+\frac{1}{3}+\frac{1}{3^2}+........+\frac{1}{3^n}\right)}=?$  

 $\lim_{x\rightarrow0}\ \ \frac{\cos x-\cos5x}{\cos2x-\cos6x}=?$  

 $\lim_{x\rightarrow2}\ \frac{\log\left(x-1\right)}{x^2-3x+2}=?$