Solve $ \lim_{n \rightarrow +\infty}\int_0^1 \frac{dx}{1+x^n}=$ :
______
______
1
举一反三
- Solve $ \lim_{x \rightarrow \infty}[x-x^2\ln{(1+\frac{1}{x}})]=$ :<br/>______
- 下面积分收敛的是 A: $\int_0^\infty \frac{x^{4/3}}{1+x^2} dx$ B: $\int_1^\infty \frac{dx}{x \sqrt[3]{1+x^3}}$ C: $\int_1^\infty \frac{1}{x} dx$ D: $\int_1^\infty \frac{\arctan x}{x} dx$
- Solve $n \in \mathbb{N}, \int_0^{\frac{\pi}{2}}(\sin^n{x}-\cos^n{x})dx=$ :<br/>______
- Solve $ \frac{1}{\pi}\int_0^{\frac{\pi}{2}}\sin^4{x}dx=$ :<br/>______
- Solve $\sum_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)}$:<br/>______
内容
- 0
Solve $\lim_{x \rightarrow 0}\frac{x\cos{x}-\sin{x}}{x^3}=$:<br/>______
- 1
Solve $\sum_{n=1}^{\infty}\frac{2n-1}{2^n}$:<br/>______
- 2
Solve $ \lim_{x \rightarrow 0^+}\frac{\cos{2\sqrt{x}-1+2x}}{x^2}=$ :<br/>______
- 3
下面级数求和错误的是 A: $\sum_{n=0}^\infty q^n = \frac{1}{1-q} (0\lt q\lt1) $ B: $\sum_{n=1}^\infty \frac{x^{2^{n-1}}}{1-x^{2^n}} = \frac{x}{1-x} (|x|\lt 1) $ C: $\sum_{n=1}^\infty \frac{1}{{n!}} = e $ D: $\sum_{n=1}^\infty \frac{x^{2^{n-1}}}{1-x^{2^n}} = \frac{1}{1-x} (x>1) $
- 4
下列广义积分中, （）是发散的。 A: \( \int_{ - \infty }^0 { { e^x}dx} \) B: \( \int_0^1 { { 1 \over {\sqrt x }}dx} \) C: \( \int_0^{ + \infty } { { e^{ - 100x}}dx} \) D: \( \int_1^{ + \infty } { { 1 \over {\sqrt x }}dx} \)