1、0.1:2*pi; x=t-sin(t);y=2*(1-cos(t); plot(x,y)7螺旋线 x=cos(t); y=sin(t); z=t;plot3(x,y,z)(8)阿基米德螺线 theta=0: rho1=(theta); subplot(1,2,1),polar(theta,rho1)(9) 对数螺线theta=0:rho1=exp(theta);subplot(1,2,1),polar(theta,rho1)(12)心形线 rho1=1+cos(theta);练习2.21. 求出下列极限值(1)syms n limit(n3+3n)(1/n) ans =3(2)syms nl
2、imit(n+2)(1/2)-2*(n+1)(1/2)+n(1/2),n,inf) 0(3)syms x; limit(x*cot(2*x),x,0) 1/2(4)syms x m;limit(cos(m/x)x,x,inf)1(5)syms x limit(1/x-1/(exp(x)-1),x,1)(exp(1)-2)/(exp(1)-1)(6) limit(x2+x)(1/2)-x,x,inf) 练习2.41. 求下列不定积分,并用diff验证:Clear syms x y y=1/(1+cos(x); f=int(y,x) f = tan(1/2*x) y=tan(1/2*x); yx=
3、diff(y,x); y1=simple(yx) y1 = 1/2+1/2*tan(1/2*x)2 syms x yy=1/(1+exp(x);f=int(y,x)f = -log(1+exp(x)+log(exp(x)y=-log(1+exp(x)+log(exp(x);yx=diff(y,x);y1=simple(yx)y1 = 1/(1+exp(x)y=x*sin(x)2; f=int(y,x) f =x*(-1/2*cos(x)*sin(x)+1/2*x)-1/4*cos(x)2-1/4*x2 syms x y y=x*(-1/2*cos(x)*sin(x)+1/2*x)-1/4*co
4、s(x)2-1/4*x2; y1=simple(yx) y1 =x*sin(x)2(4) y=sec(x)3;1/2/cos(x)2*sin(x)+1/2*log(sec(x)+tan(x)y=1/2/cos(x)2*sin(x)+1/2*log(sec(x)+tan(x);1/cos(x)32. 求下列积分的数值解1)y=int(x(-x),x,0,1)y =int(x(-x),x = 0 . 1)vpa(y,10)1.2912859972)clear y=int(exp(2*x)*cos(x)3,x, cleary=int(1/(2*pi)(1/2)*exp(-x2/2),x,0,1)y
5、= 7186705221432913/36028797018963968*erf(1/2*2(1/2)*2(1/2)*pi(1/0,2*pi)22/65*exp(pi)4-22/65vpa(ans,10)(3) syms x y=int(1/(2*pi)(1/2)*exp(-x2/2),0,1); vpa(y,14).341344746068552(4) y=int(x*log(x4)*asin(1/x2),1,3);Warning: Explicit integral could not be found. In sym.int at 582.4597721282375 2(5) y=int
6、(1/(2*pi)(1/2)*exp(-x2/2),-inf,inf);.99999999999999 练习2.51判断下列级数的收敛性,若收敛,求出其收敛值。1)syms ns1=symsum(1/n(2n),n,1,inf)s1 = sum(1/(n(2n),n = 1 . Inf)vpa(s1,10)ans = 1.062652416因此不收敛2)syms ns1=symsum(sin(1/n),n,1,inf) s1 =sum(sin(1/n),n = 1 . Inf)vpa(s1,10) 不收敛(3) syms n s=symsum(log(n)/n3,n,1,inf)s =-zet
7、a(1,3)收敛(4) syms n s1=symsum(1/(log10(n)n,n,3,inf)sum(1/(log(n)/log(10)n),n = 3 . inf)(5) syms ns1=symsum(1/n*log10(n),n,2,inf)sum(1/n*log(n)/log(10),n = 2 . Inf)(6) s=symsum(-1)n*n/n2+1,n,1,inf)sum(-1)n/n+1,n = 1 . Inf) 习题3.11)clear;x,y=meshgrid(-30:0.3:30);z=10*sin(sqrt(x.2+y.2)./sqrt(1+x.2+y.2);
8、meshc(x,y,z) x,y=meshgrid(-30: z=10*sin(x2+y2)(1/2)/(1+x2+y2)(1/2)mesh(x,y,z)1.2.取适当的参数绘制下列曲面的图形。 a=-2:2; b=-3:3; x,y=meshgrid(a,b); z=(1-(x.2)/4-(y.2)/9).(1/2); mesh(x,y,z) hold onmesh(x,y,-z) a=-1:1; b=-2:x,y=meshgrid(a,b); z=(4/9)*(x.2)+(y.2); x,y=meshgrid(-1:1); z=(1/3)*(x.2)-(1/3)*(y.2); 习题3.2P
9、49/例3.2.1命令: limit(limit(x2+y2)/(sin(x)+cos(y),0),pi),-pi2 limit(limit(1-cos(x2+y2)/(x2+y2),0),0),P49/例3.2.2clear;syms x y z dx dy dz zxz zy zxx zxyz=atan(x2*y) z =atan(x2*y) zx=diff(z,x),zy=diff(z,y)zx 2*x*y/(1+x4*y2)zy =x2/(1+x4*y2) dz=zx*dx+zy*dy,dz =2*x*y/(1+x4*y2)*dx+x2/(1+x4*y2)*dzxx=diff(zx,x
10、),zxy=diff(zx,y)zxx =2*y/(1+x4*y2)-8*x4*y3/(1+x4*y2)2zxy =2*x/(1+x4*y2)-4*x5*y2/(1+x4*y2)23.2.1作图表示函数z=x*exp(-x2-y2) (-1x1,0y2)沿x轴方向梯度 b=0: z=x.*exp(-x.2-y.2); px,py=gradient(z,0.1,0.1);contour(a,b,z),hold on, quiver(a,b,px,py),hold off 习题3.41. 解下列微分方程(1)y=dsolve(Dy=x+y,y(0)=1x-x-1+2*exp(x)x=1 2 3x = 1 2 3 -x-1+2*exp(x)3.4366 11.7781 36.1711(2)x=2*x+3*y,y=2*x+y,x(0)=-2,y(0)=2.8,0t10,做相平面图新建M函数function dy=weifen1(t,y)dy=zeros(2,1);dy(1)=2*y(1)+
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