A: t=0:4*pi, y=5cos(10t+pi/3)
B: t=0:0.1:4π, y=5*cos(10*t+π/3)
C: t=0:4π, y=5*cos(10*t+π/3)
D: t=0:0.1:4*pi, y=5*cos(10*t+pi/3)
举一反三
- 曲线$\left\{ \matrix{ {x^2} + {y^2} + {z^2} = 9 \cr y = x \cr} \right.$的参数方程为( ). A: $$\left\{ \matrix{ x = \sqrt 3 \cos t \cr y = \sqrt 3 \cos t \cr z = \sqrt 3 \sin t \cr} \right.(0 \le t \le 2\pi )$$ B: $$\left\{ \matrix{ x = {3 \over {\sqrt 2 }}\cos t\cr y = {3 \over {\sqrt 2 }}\cos t \cr z = 3\sin t \cr} \right.(0 \le t \le 2\pi )$$ C: $$\left\{ \matrix{ x = \cos t\cr y = \cos t\cr z = \sin t \cr} \right.(0 \le t \le 2\pi )$$ D: $$\left\{ \matrix{ x = {{\sqrt 3 } \over 3}\cos t\cr y = {{\sqrt 3 } \over 3}\cos t \cr z = {{\sqrt 3 } \over 3}\sin t\cr} \right.(0 \le t \le 2\pi )$$
- 计算曲线积分\({\oint_L {({x^2} + {y^2})} ^3}ds\)，其中\(L\)为圆周\(x = a\cos t,y = a\sin t(0 \le t \le 2\pi )\)。 A: \(2\pi {a^7}\) B: \(2\pi {a^6}\) C: \(2\pi {a^5}\) D: \(2\pi {a^8}\)
- 产生周期为1的三角波信号,正确的代码是 A: t=0:1/1000:5;y=sawtooth(2*pi*t,0.5);号，正确的代码是 B: t=0:1/1000:5;y=sawtooth(2*pi*10*t,0.5);，正确的代码是 C: t=0:1/1000:5;y=square(2*pi*t,0.5);� D: t=0:1/1000:5;y=square(2*pi*10*t,0.5);
- 一空间曲线由参数方程x=ty=sin(2t) , -3<t<3z=cos(3t*t)表示，绘制这段曲线可以由下列哪组语句完成。? t=-3:0.1:3;x=t;y=sin (2*t);z=cos (3*t.*t);plot3(x, y, z)|t=-3:0.1:3;x=t;y=sin (2*t);z=cos (3*t*t);plot3(x, y, z)|t=-3:0.1:3;y=sin (2*t)；z=cos (3*t.*t)；plot3 (x, y, z)|t=-3:0.1:3;x=t;y=sin (2*t);z=cos (3*t.*t);plot3(x, y, z, t)
- 一空间曲线由参数方程x=t y=sin(2t) , -3<t<3z=cos(3t*t)表示，绘制这段曲线可以由下列哪组语句完成。 A: t=-3:0.1:3;x=t;y=sin(2*t);z=cos(3*t.*t);plot3(x, y, z, t) B: t=-3:0.1:3;x=t;y=sin(2*t);z=cos(3*t*t);plot3(x, y, z) C: t=-3:0.1:3;y=sin(2*t)；z=cos(3*t.*t)；plot3(x, y, z) D: t=-3:0.1:3;x=t;y=sin(2*t);z=cos(3*t.*t);plot3(x, y, z) E: x=-3:0.1:3;y=sin(2*x);z=cos(3*x.*x);plot3(x, y, z)
内容
- 0
设\(z = f(x,y)\)，\(x = \sin t\)，\(y = {t^3}\)，则全导数\( { { dz} \over {dt}} = \) A: \({f'_x} \sin t+ 3{t^2}{f'_y}\) B: \({f'_x} \cos t+ {t^2}{f'_y}\) C: \({f'_x} \cos t+ 3{t^2}{f'_y}\) D: \({f'_y} \cos t+ 3{t^2}{f'_x}\)
- 1
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: $(0,-1,0)$
- 2
已知“syms x y z t a b; x=a*cos(t); y=a*sin(t); z=3*t; dx=diff(x,'t'); dy=diff(y,'t'); dz=diff(z,'t'); f=y*dx-x*dy+(x+y+z)*dz; t1=0; t2=2*pi; W=int(f,t,t1,t2)”,则正确的说法是【】
- 3
已知“syms s t r; I1=int(int(int(r.^4*sin(s),r,0,2*cos(s)),s,0,pi/3),t,0,2*pi); I2=int(int(int(r.^4*sin(s),r,0,1), s,pi/3,pi),t,0,2*pi); I=I1+I2”中,则下列说法正确的是【】
- 4
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: $\frac{32}{105} \pi a^2$