举一反三
- 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)
- 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: $$\left\{ \matrix{ x = {{\sqrt 3 } \over 3}\cos t\cr y = {{\sqrt 3 } \over 3}\cos t \cr z = {{\sqrt 3 } \over 3}\sin t\cr} \right.(0 \le t \le 2\pi )$$
- 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: \({f'_y} \cos t+ 3{t^2}{f'_x}\)
- 设\(z = {e^{x - 2y}}\)，而\(x = \sin t\)，\(y = {t^3}\)，则全导数\( { { dz} \over {dt}} = \) A: \({e^{\sin t - {t^3}}}(\cos t - 6{t^2})\) B: \({e^{\sin t - 2{t^3}}}(\sin t - 6{t^2})\) C: \({e^{\cos t - 2{t^3}}}(\cos t - 6{t^2})\) D: \({e^{\sin t - 2{t^3}}}(\cos t - 6{t^2})\)
- 设\(z = {e^{x - 2y}}\)，而\(x = \sin t,\;y = {t^3},\)则\( { { dz} \over {dt}} = \)( ) A: \({e^{\sin t - 2{t^3}}}\) B: \({e^{\sin t - 2{t^3}}}\left( {\cos t - 6{t^2}} \right)\) C: \({e^{\sin t - 2{t^3}}}\ {\sin t } \) D: \({e^{\sin t - 2{t^3}}}\,{t^3}\)
内容
- 0
设 $z=e^{x-2y}$, 而 $x=\sin t, y=t^3$, 则 $\displaystyle\frac{\mathrm{d}z}{\mathrm{d}t}=$ A: $\displaystyle\cos t+3t^2$ B: $e^{\sin t-2t^3}(\cos t+3t^2)$ C: $\displaystyle\cos t-6t^2$ D: $e^{\sin t-2t^3}(\cos t-6t^2)$
- 1
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【】
- 2
求微分方程[img=269x55]17da6536a9fba07.png[/img]的通解； （ ） A: (C15*sin(2*t))/exp(3*t) + (C16*sin(2*t))/exp(3*t) B: (C15*cos(2*t))/exp(3*t) - (C16*sin(2*t))/exp(3*t) C: (C15*cos(2*t))/exp(3*t) + (C16*cos(2*t))/exp(3*t) D: (C15*cos(2*t))/exp(3*t) + (C16*sin(2*t))/exp(3*t)
- 3
求解常微分方程组<img src="http://img1.ph.126.net/B8qMozAYz7oEzmWV3LBSvg==/6597340246519736485.png" />, 应用的语句是? DSolve[{x'[t]+y[t]==Cos[t],y'[t]+x[t]==Sin[t]},{x,y},t]|DSolve[{x'[t]+y[t]==Cos[t],y'[t]+x[t]==Sin[t]},x[t],y[t],t]|DSolve[{x'[t]+y[t]==Cos[t],y'[t]+x[t]==Sin[t]},{x[t],y[t]},t]|DSolve[x'[t]+y[t]=Cos[t],y'[t]+x[t]=Sin[t],{x[t],y[t]},t]
- 4
函数 [img=197x96]1803dbfc46ca27a.png[/img]表示的曲面称为椭圆锥面，绘制这个曲面的程序是： A: s=-5:0.1:5;t=-5:0.1:5;[x, y]=meshgrid(s, t);z=sqrt(x.^2+y.^2);mesh(x,y,z) B: a=3;b=2;s=-5:0.1:5;t=-5:0.1:5;[x, y]=meshgrid(s, t);z=sqrt(x.^2/a/a+y.^2/b/b);mesh(x, y, z) C: a=3;b=2;s=-5:0.1:5;t=-5:0.1:5;[x, y]=meshgrid(s, t);z=sqrt(x.^2/a*a+y.^2/b*b);mesh(x, y, z) D: a=3;b=2;s=-5:0.1:5;t=-5:0.1:5;[x, y]=meshgrid(s, t);z=sqrt(x^2/a/a+y^2/b/b);mesh(x, y, z);