A: \(y=a\)cos[\(\frac{u}{b}\)\((t-t')\)\(+\frac{\pi}{2}\)]
B: \(y=a\)cos[2\(\pi\)\(\frac{u}{b}\)\((t-t')\)\(-\frac{\pi}{2}\)]
C: \(y=a\)cos[\(\pi\)\(\frac{u}{b}\)\((t+t')\)\(+\frac{\pi}{2}\)]
D: \(y=a\)cos[\(\pi\)\(\frac{u}{b}\)\((t-t')\)\(-\frac{\pi}{2}\)]
举一反三
- 已知椭圆参数方程$x= a cos \ t, y=b sin \ t$, 则椭圆在$t=\frac{\pi}{4}$点处的斜率为 A: $\frac{b}{a}$ B: $-\frac{b}{a}$ C: $\frac{a}{b}$ D: $-\frac{a}{b}$
- 应用格林公式可计算星形线$x=a\cos^3t$, $y=a\sin^3 t$所围的平面面积为 A: $\pi a^2$ B: $\frac{3}{4}\pi a^2$ C: $\frac{3}{8}\pi a^2$ D: $\frac{3}{16}\pi a^2$
- 旋轮线$x=a(t-\sin t),y=a(1-\cos t)$的一拱($0 \le t \le 2 \pi$)的绕$x$轴旋转得到的立体的体积为 A: $\pi a^3$ B: $\frac{32}{105} \pi a^3$ C: $\pi a^2$ D: $\frac{32}{105} \pi a^2$
- 设函数$$y=y(x)$$由$$\left\{ \begin{matrix} x=a(t-\sin t), \\ y=a(1-\cos t) \\ \end{matrix} \right.$$确定,则$${y}''(x)=$$(). A: $$-\frac{1}{a(1-\cos t)}$$ B: $$-\frac{1}{a{{(1-\cos t)}^{2}}}$$ C: $$\frac{1}{a(1-\cos t)}$$ D: $$\frac{1}{a{{(1-\cos t)}^{2}}}$$
- $\int_{0}^{\frac{\text{ }\!\!\pi\!\!\text{ }}{4}}{[\cos (2t)\mathbf{i}+\sin (2t)\mathbf{j}+t\sin t\mathbf{k}]}\operatorname{dt}=$( ) A: $(\frac{1}{2},\frac{1}{2},\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ B: $(1,\frac{1}{2},\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ C: $(\frac{1}{2},1,\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ D: $(1,1,\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$
内容
- 0
曲线$x={{\sin }^{2}}t, y=\sin t\cos t, z={{\cos }^{2}}t$在$t=\frac{\text{ }\!\!\pi\!\!\text{ }}{2}$所对应的点处的切向向量为 A: $(0,-1,1)$ B: $(1,-1,0)$ C: $(0,1,1)$ D: $(0,-1,0)$
- 1
函数$f(x)=\sin x + \cos x,x \in [0,2 \pi]$的上凸区间为 A: $[0,\frac{\pi}{4}] \cup [\frac{5}{4} \pi,2 \pi] $ B: $[\frac{\pi}{4},\frac{5}{4} \pi]$ C: $[0,\frac{3}{4}\pi] \cup [\frac{7}{4} \pi,2 \pi] $ D: $[\frac{3}{4} \pi,\frac{7}{4} \pi] $
- 2
函数\(f(x) = x^2,\; x \in [-\pi,\pi]\)的Fourier级数为 A: \(\frac{\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \sin nx ,\; x \in [-\pi,\pi]\) B: \(\frac{\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \cos nx ,\; x \in [-\pi,\pi]\) C: \(\frac{2\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \sin nx ,\; x \in [-\pi,\pi]\) D: \(\frac{2\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \cos nx ,\; x \in [-\pi,\pi]\)
- 3
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: $\int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$
- 4
\(已知二元函数f(x,y)=\sin{x^2y},则\frac{\partial f}{\partial x}(1,\pi)=(\,)\) A: \(\frac{\pi}{2}\) B: \(2\pi\) C: \(-2\pi\) D: \(-\frac{\pi}{2}\)