《數(shù)學(xué)實(shí)驗(yàn)》習(xí)題及答案 習(xí)題4

習(xí)題41.把正切函數(shù)tanx和反正切函數(shù)arctanx的圖形及其水平漸近線y=-π2，y=解Matlab命令如下：x=-pi/2+0.01:0.1:pi/2-0.01;y1=tan(x);plot(x,y1)holdonx1=-4:0.1:4;y2=atan(x1);y3=-pi/2*ones(length(x1),1);y4=pi/2*ones(length(x1),1);plot(x1,y2,'r--',x1,y3,'k*',x1,y4,'o')legend('y=tan(x)','y=arctan(x)','y=-\pi/2','y=\pi/2')axis([-44-44])2.繪制下列曲線：（1）y=（2）y（3）x（4）x=解（1）clearx=-5:0.1:5;y=100./(1+x.^2);plot(x,y)（2）clearx=-10:0.1:10;y=1/(2*pi)*exp(-x.^2/2);plot(x,y)（3）clearx=-1:0.01:1;y1=sqrt(1-x.^2);y2=-sqrt(1-x.^2);plot(x,y1,x,y2)axisequal（4）cleart=-8:0.01:8;x=t.^2;y=5*t.^3;plot(x,y)3.繪制星形線x=2cos3t,y=2sin3t(0≤t≤2π)和擺線x=2t解cleart=0:0.1:2*pi;x=2*cos(t).^3;y=2*sin(t).^3;plot(x,y)title('星形線')figuret1=0:0.1:4*pi;x1=2*(t1-sin(t1));y1=2*(1-cos(t1));plot(x1,y1)title('擺線')4.繪制極坐標(biāo)方程ρ=2解cleart=0:0.1:6*pi;r=2*(1-cos(t));polar(t,r)5.在區(qū)間[-3,3]上作以下分段函數(shù)的圖形：fx=解clearfplot(@(x)x.^2,[-3,0])holdonfplot(@(x)exp(x)/4,[0,3])6.繪制球面x2+解clear[x,y,z]=sphere(100);mesh(4*x,4*y,4*z)axisequal7.繪制曲面z=x解clear[x,y]=meshgrid([-10:0.1:10]);z=sqrt(x.^2+y.^2);mesh(x,y,z)8.繪制曲面z=sinx2解clear[x,y]=meshgrid([-5:0.1:5]);z=sin(x.^2).*sin(y.^2);mesh(x,y,z)9.用mesh和surf函數(shù)繪制曲面z=x2+y2解clear[x,y]=meshgrid([-5:0.1:5]);z=x.^2+y.^2/4;subplot(1,2,1)mesh(x,y,z)subplot(1,2,2)surf(x,y,z)10.正螺面的參數(shù)方程為x=ucosv，y=usinv，解clearu=-1:0.1:1;v=0: