南邮数学实验答案

1、第一次练习题1、求的所有根。x=-5:0.01:5;y=exp(x)-3*x.2;plot(x,y);grid on fsolve(exp(x)-3*x.2,-1)equation solved.fsolve completed because the vector of function values is near zeroas measured by the default value of the function tolerance, andthe problem appears regular as measured by the gradient.ans = -0.4590 fs

2、olve(exp(x)-3*x.2,1)equation solved.fsolve completed because the vector of function values is near zeroas measured by the default value of the function tolerance, andthe problem appears regular as measured by the gradient.ans = 0.9100 fsolve(exp(x)-3*x.2,4)equation solved.fsolve completed because th

3、e vector of function values is near zeroas measured by the default value of the function tolerance, andthe problem appears regular as measured by the gradient.ans =3.73312、求下列方程的根。1) 2） 3） 1) p=1,0,0,0,5,1;r=roots(p)r = 1.1045 + 1.0598i 1.1045 - 1.0598i -1.0045 + 1.0609i -1.0045 - 1.0609i -0.1999 2)

4、 x=-10:0.01:10;y=x.*sin(x)-1/2;plot(x,y);grid on fsolve(x.*sin(x)-1/2,-6)equation solved.fsolve completed because the vector of function values is near zeroas measured by the default value of the function tolerance, andthe problem appears regular as measured by the gradient.ans = -6.3619 fsolve(x.*s

5、in(x)-1/2,-4)equation solved.fsolve completed because the vector of function values is near zeroas measured by the default value of the function tolerance, andthe problem appears regular as measured by the gradient.ans = -2.9726 fsolve(x.*sin(x)-1/2,2)equation solved.fsolve completed because the vec

6、tor of function values is near zeroas measured by the default value of the function tolerance, andthe problem appears regular as measured by the gradient.ans =0.74083) x=-3:0.01:3;y=sin(x).*cos(x)-x.2;plot(x,y);grid on fsolve(sin(x).*cos(x)-x.2,-1)equation solved.fsolve completed because the vector

7、of function values is near zeroas measured by the default value of the function tolerance, andthe problem appears regular as measured by the gradient.ans = -6.8434e-010 fsolve(sin(x).*cos(x)-x.2,1)equation solved.fsolve completed because the vector of function values is near zeroas measured by the d

8、efault value of the function tolerance, andthe problem appears regular as measured by the gradient.ans =0.70223、求解下列各题： 1） 2） 3） 4）5） 6） 1) syms x limit(x-sin(x)/x3) ans = 1/62) diff(exp(x)*cos(x),10) ans = -32*exp(x)*sin(x)3) int(exp(x2),x,0,1/2) ans = (pi(1/2)*erfi(1/2)/2 vpa(ans,17) ans = 0.54498

9、7104183622224) int(x4/(25+4*x2),x) ans = (125*atan(2*x)/5)/32 - (25*x)/16 + x3/125) taylor(sqrt(1+x),9,x,0) ans = - (429*x8)/32768 + (33*x7)/2048 - (21*x6)/1024 + (7*x5)/256 - (5*x4)/128 + x3/16 - x2/8 + x/2 + 16) diff(exp(sin(1/x),3) ans = (cos(1/x)*exp(sin(1/x)/x6 - (6*cos(1/x)*exp(sin(1/x)/x4 + (

10、6*sin(1/x)*exp(sin(1/x)/x5 - (6*cos(1/x)2*exp(sin(1/x)/x5 - (cos(1/x)3*exp(sin(1/x)/x6 + (3*cos(1/x)*sin(1/x)*exp(sin(1/x)/x6 subs(ans,2)ans = -0.58264、求矩阵 的逆矩阵 及特征值和特征向量。 a=-2,1,1;0,2,0;-4,1,3; inv(a)ans = -1.5000 0.5000 0.5000 0 0.5000 0 -2.0000 0.5000 1.0000 eig(a)ans = -1 2 2 p,d=eig(a)p = -0.70

11、71 -0.2425 0.3015 0 0 0.9045 -0.7071 -0.9701 0.3015d = -1 0 0 0 2 0 0 0 25、已知分别在下列条件下画出的图形：、(1) x=-10:0.01:10; y1=1/sqrt(2*pi).*exp(-x.2/2); y2=1/sqrt(2*pi).*exp(-(x+1).2/2); y3=1/sqrt(2*pi).*exp(-(x-1).2/2); plot(x,y1,x,y2,x,y3)(2) x=-10:0.01:10; y1=1/sqrt(2*pi).*exp(-x.2/2); y2=1/(sqrt(2*pi)*2).*e

12、xp(-x.2/(2*22); y3=1/(sqrt(2*pi)*4).*exp(-x.2/(2*42); plot(x,y1,x,y2,x,y3)6、画 下列函数的图形：（1） (2) （3）(1) ezmesh(u*sin(t),u*cos(t),t/4,0,20,0,2);axis equal;(2) ezmesh(x,y,sin(x*y),0,3,0,3);axis equal;(3) ezmesh(sin(t)*(3+cos(u),cos(t)*(3+cos(u),sin(u),0,2*pi,0,2*pi);axis equal;第二次练习题1、 设，数列是否收敛？若收敛，其值为多少

13、？精确到6位有效数字。 f=inline(x+7/x)/2); x0=3; for i=1:20x0=f(x0);fprintf(%g,%gn,i,x0);end1,2.666672,2.645833,2.645754,2.645755,2.645756,2.645757,2.645758,2.645759,2.6457510,2.6457511,2.6457512,2.6457513,2.6457514,2.6457515,2.6457516,2.6457517,2.6457518,2.6457519,2.6457520,2.645752、设 是否收敛？若收敛，其值为多少？精确到17位有效数

14、字, f=inline(1/n8); x1=0;for i=1:150x1=x1+f(i);fprintf(%g,%1.16fn,i,x1);end1,1.00000000000000002,1.00390625000000003,1.00405866579027594,1.00407392457933845,1.00407648457933846,1.00407707995351927,1.00407725342004488,1.00407731302468969,1.004077336255262610,1.004077346255262611,1.004077350920336512,1

15、.004077353246016813,1.004077354471911514,1.004077355149515015,1.004077355539699316,1.004077355772530017,1.004077355915883518,1.004077356006628119,1.004077356065508520,1.004077356104571121,1.004077356131010122,1.004077356149233123,1.004077356162002724,1.004077356171087425,1.004077356177641026,1.004077356182429727,1.004077356185970428,1.004077356188617429,1.004077356190616430,1.004077356