12.3 Limit of Infinities 无穷的极限 - 独中课程 | 线上补习

高二数学 | 高级数学

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12.3 Limit of Infinities 无穷的极限

Evaluate the following limit.
计算下列各极限

[1]

$\lim\limits_{x\rightarrow\infty}\frac{5-2x-x^3}{4+3x^2+2x^3}$

$-\frac{1}{2}$

[2]

$\lim\limits_{x\rightarrow\infty}\frac{3x^2-2x-1}{2x^3-x^2+5}$

[3]

$\lim\limits_{x\rightarrow+\infty}\frac{x^3-8x^2+4x-2}{x^2-6x+3}$

$+\infty$

[4]

$\lim\limits_{x\rightarrow\infty}(\sqrt{x^4+1}-x^2)$

[5]

$\lim\limits_{x\rightarrow-\infty}\frac{-x^5+3x^2-2}{3x^4-5x-4}$

$+\infty$

[6]

$\lim\limits_{x\rightarrow-\infty}\frac{2x-\sqrt{x^2+1}}{3x-1}$

[7]

$\lim\limits_{x\rightarrow\infty}\frac{\sqrt{2x+1}-\sqrt{x+3}}{\sqrt{4x-1}+\sqrt{x-1}}$

$\frac{\sqrt2-1}{3}$

[8]

$\lim\limits_{x\rightarrow-\infty}\frac{\sqrt{4x^2-2x+1}}{x}$

-2

[9]

$\lim\limits_{n\rightarrow\infty}sin{\sum\limits_{i=1}^{n}\frac{\pi}{2^{i+1}}}$

[10]

$\lim\limits_{n\rightarrow\infty}\sum\limits_{i=1}^{n}\frac{3^i-2^i}{6^i}$

$\frac{1}{2}$

[11]

If $\lim\limits_{x\rightarrow\infty}\frac{ax^3+bx^2-4}{2x^2+3x-1}=\frac{1}{3}$ , find the values of a and b.

若 $\lim\limits_{x\rightarrow\infty}\frac{ax^3+bx^2-4}{2x^2+3x-1}=\frac{1}{3}$ , 求a 和b的值.

0 , $\frac{2}{3}$