1. $\mathop {\lim }\limits_{x \to 1}\frac{x^{100}-2x+1}{x^{50}-2x+1}$2. $\mathop {\lim }\limits_{x \to a}\frac{(x^n-a^n)-na^{n-1}(x-a)}{(x-a)^2} (n\in N^*)$
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. $\mathop {\lim }\limits_{x \to \pm \infty }\frac{\left| {1+x-3x^2} \right|-\left| {x} \right|}{\left| {1-2x} \right|+\left| {x^2+3x} \right|}$