1) $\mathop {\lim }\limits_{x \to 1}$ $\frac{(1-\sqrt{x})(1-\sqrt[3]{x})...(1-\sqrt[n]{x})}{(1-x)^{n-1}}$ KQ: $\frac{1}{n!}$
2)$\mathop {\lim }\limits_{x \to 0}$ $\frac{(\sqrt{1+x^{2}}+x)^{2009} - (\sqrt{1+x^{2}}-x)^{2009}}{x}$ KQ: 4018
3) $\mathop {\lim }\limits_{x \to 1}$ $(\frac{2011}{1-x^{2011}}-\frac{2012}{1-x^{2012}})$ KQ: $\frac{-1}{2}$
4)$\mathop {\lim }\limits_{x \to 1}$ $\frac{x^{2}-4}{\cos \frac{\pi x}{4}}$ KQ: $\frac{-16}{\pi }$
5)$\mathop {\lim }\limits_{x \to 1}$ $[(1+x)(1+x^{2})(1+x^{4}...(1+x^{2})]$ với $\left| {x} \right|$ <1 KQ: $\frac{1}{1-x}$