习题3：

1.

>> syms x f

>>

f=limit((cos(sqrt(x)))^(pi/x),x,0,'right')

f =exp(-1/2*pi)

2.

>> syms x f

>>

f=limit((3*sin(x)+x^2*cos(1/x))/((1+cos(x))*log(1+x)),x,0)

f = 3/2

3.

>> syms x f

>>

f=limit((sqrt(4*x^2+x-1)+x+1)/sqrt(x^2+sin(x)),x,-inf)

f = 1

4.

>> syms x y f

>>

f=limit(limit((x^2+y^2)^(x^2*y^2),x,0),y,0)

f =1

5.

>> syms x y f

>>

y=(tan(sqrt(x+sqrt(x+sqrt(2*x)))))^2

y =tan((x+(x+2^(1/2)*x^(1/2))^(1/2))^(1/2))^2

>> f=diff(y)

f =

tan((x+(x+2^(1/2)*x^(1/2))^(1/2))^(1/2))*(1+tan((x+(x+2^(1/2)*x^(1/2))^(1/2))^(1/2))^2)/(x+(x+2^(1/2)*x^(1/2))^(1/2))^(1/2)*(1+1/2/(x+2^(1/2)*x^(1/2))^(1/2)*(1+1/2*2^(1/2)/x^(1/2)))

6.

>> syms x y f

>> y=(cos(x^2))*(sin(1/x))^2

y =cos(x^2)*sin(1/x)^2

>> f=diff(y)

f =

-2*sin(x^2)*x*sin(1/x)^2-2*cos(x^2)*sin(1/x)*cos(1/x)/x^2

7.

>> syms x f

>>

f=int(sqrt(sin(x)-(sin(x))^3),'x',0,pi)

f =4/3

8.

>> syms x f

>>

f=int(1/x*sqrt((x+1)/(x-1)))

f =

((1+x)/(x-1))^(1/2)*(x-1)/((1+x)*(x-1))^(1/2)*(-atan(1/(x^2-1)^(1/2))+log(x+(x^2-1)^(1/2)))

9.

> syms x y f

>>

f=dsolve('D2y+4*Dy+4*y=exp(-2*x)','x')

f =

1/2*x^2*exp(-2*x)+C1*exp(-2*x)+C2*exp(-2*x)*x

10.

>> syms x y f

>>

f=dsolve('x^2*Dy+x*y=y^2','y(1)=1','x')

f = 2*x/(1+x^2)

习题4：

1.

>> A=[1 2 4 0 5 10 11 21 3 1];

>> plot(A)

2.

(1)

t=[0:0.01:2*pi];

x=sin(t);

y=cos(t);

plot(x,y)

axis([-1.5 1.5 -1.5 1.5])

%限定x轴和y轴的显示范围

grid on

axis('equal')

(2)

t=0:0.1:2*pi;

x=sin(t);

y=cos(t);

z=x+y*i;

plot(z)

axis equal

3. 已知伏安曲线为U=IR, R分别为1欧姆，5欧姆，10欧姆，20欧姆。

(1)在一张图上画出I 在(0-2Π)范围内的U曲线，

(2)添加标题“伏安曲线U=IR”

(3)添加横纵座标的单位“安培”，“伏特”；

(4)添加标出每条线代表的方程。

I=0:pi/20:2*pi;

R1=1.0;

R2=5.0;

R3=10.0;

R4=20.0;

U1=I*R1;

U2=I*R2;

U3=I*R3;

U4=I*R4;

plot(I,U1,I,U2,I,U3,I,U4);

plot(I,U1,I,U2,I,U3,I,U4);

title('伏安曲线U=IR');

xlabel('安培');

ylabel('伏特');

legend('U=I','U=5I','U=10I','U=20I');

4. file---import data---4---A4

x=A4(:,1);

y=[A4(:,2) A4(:,3)];

bar(x,y)

5. A=[1 1 1 1 1 1 1

1 2 2 2 2 2 1

1 2 2 3 2 2 1

1 2 2 2 2 2 1

1 1 1 1 1 1 1];

>> plot(A)

>> bar(A)

6. x=-1:0.01:1;

y=-1:0.01:1;

[X,Y]=meshgrid(x,y);

Z=X.^2+Y.^2;

surf(X,Y,Z);

7. [X,Y,Z]=ELLIPSOID(0,0,0,2,3,4);

surf(X,Y,Z)

view([0 0 1])

view([0 1 0])

to try SPHERE and CYLINDER yourself