1. lim2. \mathop {\lim }\limits_{x \to a}\frac{(x^n-a^n)-na^{n-1}(x-a)}{(x-a)^2} (n\in N^*)
3. \mathop {\lim }\limits_{x \to 1}\frac{x^n-nx+n-1}{x^2-2x+1} (n\in N^*)
4. \mathop {\lim }\limits_{x \to 1}(\frac{1}{1-x}-\frac{n}{1-x^n}) (n\in N^*)
5. \mathop {\lim }\limits_{x \to 0}\frac{\sqrt{a+x}+\sqrt{a}}{x}
6. \mathop {\lim }\limits_{x \to a}\frac{\sqrt{x}-\sqrt{a}+\sqrt{x-a}}{x^2-a^2}
7. \mathop {\lim }\limits_{x \to 0}\frac{\sqrt[n]{1+x}-1}{x} (n\in N^*,n\geq 2)
8. \mathop {\lim }\limits_{x \to 0}\frac{\sqrt[n]{a+x}-\sqrt[n]{a}}{x} (n\in N^*,n\geq 2)
9. \mathop {\lim }\limits_{x \to \pm \infty }\frac{(x+1)^{10}+(x+2)^{10}+...+(x+100)^{10}}{x^{10}+10^{10}}
10. \mathop {\lim }\limits_{x \to \pm \infty }\frac{\left| {1+x-3x^2} \right|-\left| {x} \right|}{\left| {1-2x} \right|+\left| {x^2+3x} \right|}