一,e0.001的近似值是：二,lim(x→0)sin3x/x的极限三,lim(x→0)xsin1/x的极限
1.e^x=1+x/1!+x^2/2!+x^3/3!+...取x=0.001得e^0.001=1+0.001+0.001^2/2!+0.001^3/3!+...误差Rn=0.001^(n+1)/(n+1)!+0.001^(n+2)/(n+2)!+0.001^(n+3)/(n+3)!+...
举一反三
- 求极限\( \lim \limits_{x \to 0} { { {x^2}\sin {1 \over x}} \over {\sin x}}{\rm{ = }}\)______
- 【单选题】极限 lim x → 0 1 − cos 3 x x sin 3 x 的值为? A. 0 B. 1/6 C. 2/3 D. 3/2
- ①lim(x→∞)sin(1/x)/(1/x)等于多少?②lim(x→0)sin(1/x)/(1/x)等于多少?
- lim xcot x;x +0极限
- 求极限\( \lim \limits_{x \to {0^{\rm{ + }}}} {\left( {\cot x} \right)^{\sin x}}{\rm{ = }}\)__________
内容
- 0
2.极限$\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,{{x}^{\sin x}}$( )。 A: 等于$1$ B: 等于$0$ C: 等于$-1$ D: 不存在
- 1
求函数极限lim(x→0)(1-sinx)^1/x
- 2
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: \(\lim \limits_{x \to \infty } {(1 - {1 \over {2x}})^{2x}} = e\)
- 3
求下列极限：(1)lim(x→0)(∫x0ln(1＋2t^2)dt／x^3
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计算极限lim(x趋向于无穷大){[(a^x)+1]/x}^1/x,(a＞0,a不等于1)