Solve $\lim_{x \rightarrow 0}\frac{x\cos{x}-\sin{x}}{x^3}=$:
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-1/3
举一反三
- Solve $ \lim_{x \rightarrow 0^+}\frac{\cos{2\sqrt{x}-1+2x}}{x^2}=$ :<br/>______
- Solve $ \lim_{x \rightarrow \infty}[x-x^2\ln{(1+\frac{1}{x}})]=$ :<br/>______
- \({\lim_{x\to0}}\)\({\lim_{y\to0}}\)\(\frac{sin(x^2+y^2)}{x^2+y^2}\)= <br/>______
- 求函数$f(x)=x^{\sin x}$的导数 A: $x^{\cos x}$ B: $\sin (x) x^{\sin (x) -1}$ C: $x^{\sin x}(\cos x\ln x+\frac{\sin x}{x})$ D: $x^{\sin x}(\sin x\ln x+\frac{\cos x}{x}$
- $\int \sin^3 x \cos x dx = $ A: $\frac{\sin^4 x}{4} +C$ B: ${\sin^4 x} +C$ C: $\frac{\cos^4 x}{4} +C$ D: $\frac{\cos^4 x}{4} +C$
内容
- 0
\( \lim \limits_{x \to 0} { { \sqrt {1 + x\sin x} - \cos x} \over { { {\sin }^2}{x \over 2}}} = \)______ 。
- 1
Solve $n \in \mathbb{N}, \int_0^{\frac{\pi}{2}}(\sin^n{x}-\cos^n{x})dx=$ :<br/>______
- 2
8. 下列不等式正确的是 A: $0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}$ B: $0\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$ C: $\int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}$ D: $\int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$
- 3
\({\lim_{x\to0}}\)\({\lim_{y\to0}}\)(x+y)sin\(\frac{1}{x^2+y^2}\) <br/>______
- 4
\({\lim_{x\to 0}}\)\({\lim_{y\to 0}}\)\(\frac{xy}{x^2+y^2}\) <br/>______