为什么lim(x→∞)(1-1/x)^3=1?
x趋近于无限大的时候,1/x则趋近于0,则1-0=1,1的三次方当然还是1做这种极限的题,基本上就是把1/∞看成是0
举一反三
- lim(x→∞)(1-1/(x+1))^(-x-1)=lim(x→∞)(1/(x+1))^(-x-1)lim(x→∞)(1-1/（x+1）)^(x+1)
- 【单选题】若 f ( x ) = ( x − 1 ) x 2 − 1 2 , g ( x ) = x − 1 x + 1 ,则? A. f ( x ) = g ( x ) "> f ( x ) = g ( x ) B. lim x → 1 f ( x ) = g ( x ) "> lim x → 1 f ( x ) = g ( x ) C. lim x → 1 f ( x ) = lim x → 1 g ( x ) "> lim x → 1 f ( x ) = lim x → 1 g ( x ) D. 以上等式均不成立
- ①lim(x→∞)sin(1/x)/(1/x)等于多少?②lim(x→0)sin(1/x)/(1/x)等于多少?
- 当x趋于0时,lim（1+X）^(1/X^2)和lim（1+X）^(1/X^3)中无穷大量是?
- 下列极限计算正确的是( ). A: \(\lim \limits_{x \to 0} { { \left| x \right|} \over x} = 1\) B: \(\lim \limits_{x \to {0^ + }} { { \left| x \right|} \over x} = 1\) C: \(\lim \limits_{x \to 0} {(1 - {1 \over {2x}})^{2x}} = {e^{ - 1}}\) D: \(\lim \limits_{x \to \infty } {(1 - {1 \over {2x}})^{2x}} = e\)
内容
- 0
lim(x趋向1)(x+2)/{(x^2)-1}=
- 1
\( \lim \limits_{x \to 0} { { x - \sin x} \over { { x^3}}} \)=( ) A: 0 B: 1 C: 6 D: \( {1 \over 6} \)
- 2
lim(fx-x^3)/x^2=2,limfx/x=1,求fx
- 3
\(\lim \limits_{x \to 1} { { \sin \left( { { x^2} - 1} \right)} \over {x - 1}}{\rm{ = }}\)______ 。
- 4
\( \lim \limits_{x \to 0} { { x - \arcsin x} \over { { {\sin }^3}x}} = {1 \over 6} \)