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Question

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.

$\mathop {\lim }\limits_{x \to \pm \infty }\frac{\left| {1+x-3x^2} \right|-\left| {x} \right|}{\left| {1-2x} \right|+\left| {x^2+3x} \right|}$

ai lam bdt k t post cho. tai lieu hoi thao cua truong chuyen Tran Phu Hai Phong lun.
Làm ko? Tớ có cả trăm bài giới hạn. Làm mỏi tay luôn :))

Trần Nhật Tân · Answer 1 · 4/30/2014 9:38:50 PM

7.

$\mathop {\lim }\limits_{x \to 0}\dfrac{\sqrt[n]{1+x}-1}{x}$

$=\mathop {\lim }\limits_{x \to 0}\dfrac{\dfrac{x}{\sqrt[n]{(1+x)^{n-1}}+\ldots+\sqrt[n]{1+x}+1}}{x}$

$=\mathop {\lim }\limits_{x \to 0}\dfrac{1}{\sqrt[n]{(1+x)^{n-1}}+\ldots+\sqrt[n]{1+x}+1}=\dfrac{1}{n}$

Trả lời 30-04-14 09:38 PM

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