大连理工大学高等数学A matlab上机

19年的。时间太久，题目找不到了。

求极限
1.
>>syms x;
>> limit(sin(sin(x))/x-1,x,0)ans=0
2．
>>syms n;
>> limit(tan(pi/4+1/n)^n,n,inf)
ans=exp(2)
3．
>>syms x;
>> limit(x*(pi/2-asin(x/(sqrt(x*x+1)))),x,inf)
ans=1
4．(1) 
>>syms x;
>> limit(1/(1+exp(1/(x-1))),x,1,'left')ans=1
(2) 
>>syms x;
>> limit(1/(1+exp(1/(x-1))),x,1,'right')ans=0
级数求和
1.
>> syms x n;
>> f=1/n^2;
>> s=symsum(f,n,1,inf)ans =pi^2/6
2.
>> syms x n;
>> f=((-1)^(n+1))/(2^n);
>> s=symsum(f,n,0,inf)ans =-2/3
3.
>> syms x n;
>> f=((-1)^(n+1)*x^(n+1))/(n*(n+1));
>> s=symsum(f,n,1,inf)ans =piecewise([abs(x) <= 1, (x^2*hypergeom([1, 1], [3], -x))/2])
泰勒展式
1.
>>syms x;
>> y=taylor(sin(x),'Order',3);
>> x=3*pi/180;
>> eval(y)
ans=0.0524
2.
>>syms x;
>> y=taylor(x^(1/3),x,30,'Order',3)
y=30^(1/3) + (30^(1/3)*(x - 30))/90 - (30^(1/3)*(x - 30)^2)/8100
>> x=30;
>> eval(y)
ans =3.1072
3.
>>syms x;
>> y=taylor(x^(1/2),x,4,'Order',2)
y =x/4 + 1
>> x=4.4;
>> eval(y)
ans=2.1000
多元函数微分
1.
>> syms x y z;
>> f=sqrt(x^2+y^2)-z;
>> u=diff(f,x);
>> v=diff(f,y);
>> x=1;
>> y=1;
>> z=sqrt(2);
>> a=eval(u);
>> b=eval(v);
>> t=-2:0.1:4;
>> x3=a*t+1;
>> y3=b*t+1;
>> z3=-t+sqrt(2);
>> [x,y]=meshgrid(-2:0.1:3);
>> z1=sqrt(x.^2+y.^2);
>> z2=a*(x-1)+b*(y-1)+sqrt(2);
>> mesh(x,y,z1)
>> hold on
>> mesh(x,y,z2)
>> hold on
>> plot3(x3,y3,z3)

2.
(u)
>> [x,y]=meshgrid(-2:0.01:2);
>> u=x.^2-y.^2;
>> mesh(x,y,u)
>> hold on
>> x1=linspace(-2,2,25);
>> y1=linspace(-2,2,25);
>> [x,y]=meshgrid(x1,y1);
>> z1=x.^2-y.^2;
>> h=contour(z1);

(v)
>> [x,y]=meshgrid(-2:0.001:2);
>> v=2*x.*y;
>> mesh(x,y,v)
>> hold on
>> x1=linspace(-2,2,25);
>> y1=linspace(-2,2,25);
>> [x,y]=meshgrid(x1,y1);
>> z2=2*x.*y;
>> h=contour(z2);

3.
>> x1=linspace(-10,10,1000);
>> y1=linspace(-10,10,1000);
>> [x,y]=meshgrid(x1,y1);
>> f=x.^4-8*x.*y+2*y.^2-3;
>>h=contour(f);