基础实验二_高等数学_1

1、实验二：用MATLAB求解高等数学问题-1姓名： 学号： 专业： 成绩： 一、实验名称：用MATLAB求解高等数学基本计算问题-1二、实验目的：1学会利用MATLAB求解极限问题；2学会利用MATLAB求解导数、偏导数和高阶导数问题；3. 学会利用MATLAB求解有关不定积分，定积分问题；4. 学会利用MATLAB求解二重积分和三重积分问题；5. 学会利用MATLAB求解极值和最值问题；6. 学会利用MATLAB解决微分法在几何上的应用；7. 学会利用MATLAB求解有关泰勒级数展开问题。三、实验准备：复习高等数学中相关主题的理论知识和方法。四、实验内容1求极限；2设，求；3计算下列积分：（1

2、）； （2）；4计算三重积分，其中是由面上的直线及曲线所围成的平面图形绕轴旋转一周而成的空间闭区域。注：需要画出被积区域的空间图形。5作出函数的图形，观察极限点、最值点的位置并求出，给出函数的单调区间；6求二元函数在点附近的极小值；7求圆柱螺旋线在对应点处的切线方程和法平面方程；8求球面在点处的切平面及法线方程；9用命令观测函数的麦克劳林展开式的第4,8,12,16项，然后在同一坐标系作出函数和它展开式的前几项构成的多项式函数的图形，观测这些多项式函数的图形向的图形逼近情况。&10某个阿拉伯国家有一座著名的伊斯兰清真寺，它以中央大厅的金色巨大拱形圆顶名震遐迩。因年久失修，国王下令将清真

3、寺顶部重新贴金箔装饰。据档案记载，大厅的顶部形状为半球面，其半径为30米。考虑到可能的损耗和其他技术因素，实际用量将会比清真寺顶部面积多1.5%。据此，国王的财政大臣拨出了可制造5800平方米有规定厚度金箔的黄金。建筑商人哈桑略通数学，他计算了一下，觉得黄金会有盈余。于是他以较低的承包价得到了这项装饰工程。但在施工前的测量中，工程师发现清真寺顶部实际上并非一个精确的半球面，而是一个半椭球面，其半立轴恰是30米，而半长轴和半短轴分别是30.6米和29.6米。这一来，哈桑犯了愁，他担心黄金是否还有盈余？甚至可能短缺，最后的结果究竟如何呢？提示：若在直角坐标系下直接积分有困难，可考虑下面三种方法：方

4、法一：在极坐标系下进行积分，考虑广义极坐标法；方法二：在直接坐标系下积分，考虑蒙特卡洛方法（随机投点法）；方法三：&数值积分方法。五、程序及实验结果1. 程序：syms xlimit(sqrt(x2+x)-x,x,inf)输出结果：ans =1/22. 程序：syms x y z zx zxx zxyz=atan(x+y);zx=diff(z,x);zxx=diff(zx,x)zxy=diff(zx,y) 输出结果：zxx =-(2*x + 2*y)/(x + y)2 + 1)2zxy =-(2*x + 2*y)/(x + y)2 + 1)23.（1）程序：clearsyms x yy

5、=(sec(x)3f=int(y,x)输出结果：f =log(tan(pi/4 + x/2)/2 + tan(x)/(2*cos(x)（2）程序：syms t rs=int(r*cos(t)+r*sin(t)+1)*r,r,0,2*cos(t);q=int(s,t,-pi/2,pi/2)输出结果：q =2*pi4. 程序：clear;z=linspace(0,2,40);t=linspace(0,2*pi,40);z1,t1=meshgrid(z,t);x=sqrt(1+(z1-1).2).*cos(t1);y=sqrt(1+(z1-1).2).*sin(t1);surf(x,y,z1);sy

6、ms zm=1/2*int(pi*(1+(z-1)2)2,z,0,2) 输出结果：m=(28*pi)/155. 程序：syms xezplot('x2*sin(x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2)x1,f1=fminsearch('-x2*sin(x2-x-2)',-1.554)x2,f2=fminsearch('x2*sin(x2-x-2)',-0.754)x3,f3=fminsearch('-x2*sin(x2-x-2)',0)x4,f4=fmins

7、earch('x2*sin(x2-x-2)',1.62)syms xm=subs('x2*sin(x2-x-2)',x,-2)n=eval(m)输出结果：x1 =-1.5326 f1 =-2.2364x2 =-0.7315 f2 =-0.3582x3 =0 f3 =0x4 =1.5951 f4 =-2.2080X-2-2 -1.5326-1.5326-1.5326-0.7315-0.7315-0.73150001.59511.59511.595122Y-3.02722.2364-0.35820-2.20800增减性6. 程序：fun=inline('x(

8、1)4+x(2)2-4*x(1)*x(2)+4*x(1)+x(2)-9');x,g=fminsearch(fun,-1,-1)输出结果：x = -1.6980 y=-3.8961g =-22.65807. 程序：syms x y z t r kx1=r*cos(t);y1=r*sin(t);z1=k*t;S1=jacobian(x1,y1,z1,t);t=pi/2;x0=r*cos(t);y0=r*sin(t);z0=k*t;s0=subs(S1);syms t r kF=-x;y;z+x0;y0;z0+s0*t,G=x-x0,y-y0,z-z0*s0 输出结果：F = (496775

9、7600021511*r)/81129638414606681695789005144064 - x - r*t r - y (pi*k)/2 - z + k*tG =r*(4967757600021511*r)/81129638414606681695789005144064 - x) + k*(z - (pi*k)/2)8. 程序：syms t y x zf=x2+2*y2+3*z2-36;x0=1;y0=2;z0=3;w=x,y,z;s1=jacobian(f,w);v1=subs(s1,x,x0);z2=subs(v1,y,y0);n=subs(z2,z,z0);f=x-x0,y-y0

10、,z-z0*n'G=-x;y;z+x0;y0;z0+n'.*t输出结果：f =2*x + 8*y + 18*z - 72G = 2*t - x + 1 8*t - y + 2 18*t - z + 39.程序：clearx=-pi:0.1:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/3

11、15 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f,x,t1,'',x,t2,'*',x,t3,x,t4)输出结果：t1 =x2t2 =(2*x6)/45 - x4/3 + x2t3 =（2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2t4 =(4*x14)/42567525 - (2*x12)/467775 + (2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x210. 程序：（1）figure;clear;p=30.6;q=29.8;z=linspa

12、ce(0,30,40);t=linspace(0,2*pi,40);z1,t1=meshgrid(z,t);x=p*sqrt(z1/30).*cos(t1);y=q*sqrt(z1/30).*sin(t1);mesh(x,y,z1);（2）a= 30.6; b= 29.6; syms r e y1= int(r/sqrt(1-r2),0,1);g1= a*b*int(y1,e,0,2*pi); y2= int( (A*cos(e)2+B*sin(e)2)*r3/(2*sqrt(1-r2),r,0,1); g2= a*b*int(y2,e,0,2*pi);y3= int( (A*cos(e)2+

13、B*sin(e)2)2*r5/(8*sqrt(1-r2),r,0,1);g3= a*b*int(y3,e,0,2*pi); S= double(g1+g2-g3) 输出结果：（1）（2）S =5.6798e+003%- 14-7-16 下午12:29 -%- 14-7-16 下午2:46 -%clcsyms xlimit(sqrt(x2+x)-x,x,inf)syms x y z zx zxx zxyz=atan(x+y);zx=diff(z,x);zxx=diff(zx,x)zxy=diff(zx,y)cclclcclearsyms x yy=(sec(x)3f=int(y,x)clears

14、yms x yf=int(x+y+1,y,-sqrt(1-(x-1)2),sqrt(1-(x-1)2);m=int(f,x,0,2)clearr=linspace(0,sqrt,50);t=linspace(0,2*pi,50);R,T=meshgrid(r,t);x=R.*cos(T);y=R.*sin(T);z=sqrt(y.2+x.2+1)-1;mesh(x,y,z)syms xezplot('x2*sin(x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2);f=inline('x2*sin(x2-x

15、-2)','x');x,f=fminsearch(f,-0.7);ff=inline('-x2*sin(x2-x-2)','x');x,f=fminbnd(ff,-2,2)fun=inline('x(1)4+x(2)2-4*x(1)*x(2)+4*x(1)+x(2)-9');x,g=fminsearch(fun,-1,-1)syms x y z tx1=4*cos(t);y1=4*sin(t);z1=2*t;S1=jacobian(x1,y1,z1,t);t=pi/2;x0=4*cos(t);y0=4*sin(t);z0=

16、2*t;s0=subs(S1);syms tF=-x;y;z+x0;y0;z0+s0*t,G=x-x0;y-y0;z-z0*s0clcclearsyms t y x zf=x2+2*y2+3*z2-36;x0=1;y0=2;z0=3w=x,y,z;s1=jacobian(f,w);v1=subs(s1,x,x0);z2=subs(v1,y,y0);n=subs(z2,z,z0);f=x-x0,y-y0,z-z0*n',G=-x;y;z+x0;y0;z0+n'.*tclearsyms xf=sin(x)2;t1=taylor(f,4,x)t2=taylor(f,8,x)t3=ta

17、ylor(f,12,x)t4=taylor(f,16,x)clcclearsyms xf=sin(x)2;t1=taylor(f,4,x)t2=taylor(f,8,x)t3=taylor(f,12,x)t4=taylor(f,16,x)explot(x,f,x,t1,'*',x,t2,'',x,t3,'#',x,t4,'')clearsyms xf=sin(x)2;t1=taylor(f,4,x)t2=taylor(f,8,x)t3=taylor(f,12,x)t4=taylor(f,16,x)plot(x,f,x,t1,

18、9;*',x,t2,'',x,t3,'#',x,t4,'')clcclearsyms xf=sin(x)2;t1=taylor(f,4,x)t2=taylor(f,8,x)t3=taylor(f,12,x)t4=taylor(f,16,x)plot('f','t1','*','t2','','t3','#','t4','')clcclearsyms xf=sin(x)2;t1=taylor(f,4

19、,x)t2=taylor(f,8,x)t3=taylor(f,12,x)t4=taylor(f,16,x)clearsyms xf=sin(x)2;t1=taylor(f,4,x)t2=taylor(f,8,x)t3=taylor(f,12,x)t4=taylor(f,16,x)clearx=-10:0.1:10;f=sin(x).2;t1 =x.2t2 =(2.*x.6)./45 - x.4./3 + x.2t3 =(2.*x.10)./14175 - x.8/315 + (2.*x.6)./45 - x.4/3 + x.2t4 =(4.*x.14)/42567525 - (2.*x.12)

20、/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2plot(x,f,x,t1,'*',x,t2,'&',x,t3,'',x,t4,'#')clcclearsyms xf=sin(x)2;t1=taylor(f,4,x)t2=taylor(f,8,x)t3=taylor(f,12,x)t4=taylor(f,16,x)clearx=-10:0.1:10;f=sin(x).2;t1 =x.2t2 =(2.*x.6)./45 - x.4./3 + x.2

21、t3 =(2.*x.10)./14175 - x.8./315 + (2.*x.6)./45 - x.4./3 + x.2t4 =(4.*x.14)./42567525 - (2.*x.12)./467775 + (2.*x.10)./14175 - x.8./315 + (2.*x.6)./45 - x.4./3 + x.2plot(x,f,x,t1,'*',x,t2,'&',x,t3,'',x,t4,'#')clcx=-10:0.1:10;f=sin(x).2;t1 =x.2t2 =(2.*x.6)./45 - x.4

22、./3 + x.2t3 =(2.*x.10)./14175 - x.8./315 + (2.*x.6)./45 - x.4./3 + x.2t4 =(4.*x.14)./42567525 - (2.*x.12)./467775 + (2.*x.10)./14175 - x.8./315 + (2.*x.6)./45 - x.4./3 + x.2plot(x,f,x,t1,'*',x,t2,'&',x,t3,'',x,t4,'#')clclcclearx=-10:0.1:10;f=sin(x).2;t1 =x.2t2 =(2

23、.*x.6)./45 - x.4./3 + x.2t3 =(2.*x.10)./14175 - x.8./315 + (2.*x.6)./45 - x.4./3 + x.2t4 =(4.*x.14)./42567525 - (2.*x.12)./467775 + (2.*x.10)./14175 - x.8./315 + (2.*x.6)./45 - x.4./3 + x.2plot(x,f)clcsyms xf=sin(x)2;t1 =x2t2 =(2*x6)/45 - x4/3 + x2t3 =(2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2t4

24、 =(4*x14)/42567525 - (2*x12)/467775 + (2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2ezplot('f',-8,8)syms xf=sin(x)2;t1 =x2t2 =(2*x6)/45 - x4/3 + x2t3 =(2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2t4 =(4*x14)/42567525 - (2*x12)/467775 + (2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2ezplot(&#

25、39;f')clcsyms xf=sin(x)2;t1 =x2t2 =(2*x6)/45 - x4/3 + x2t3 =(2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2t4 =(4*x14)/42567525 - (2*x12)/467775 + (2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2ezplot('f')hold onezplot('t1')hold onezplot('t2')hold onezplot('t3')hold

26、 offclearsyms xf=sin(x)2;t1 =x2;t2 =(2*x6)/45 - x4/3 + x2;t3 =(2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2;t4 =(4*x14)/42567525 - (2*x12)/467775 + (2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2;ezplot('f') hold onezplot('t1') hold onezplot('t2') hold onezplot('t3')

27、hold offclcclearsyms xf=sin(x)2;t1 =x2;t2 =(2*x6)/45 - x4/3 + x2;t3 =(2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2;t4 =(4*x14)/42567525 - (2*x12)/467775 + (2*x10)/14175 - x8/315 + (2*x6)/45 - x4/3 + x2;%ezplot('f')ezplot('t1')%ezplot('t2')%ezplot('t3')syms t rs=int(i

28、nt(r*cos(t)+r*sin(t)+1)*r,r,0,2*cos(t),t,-pi/2,pi/2)s=int(int(r*cos(t)+r*sin(t)+1)*r,r,0,2*cos(t),t,-pi/2,pi/2)syms t rs=int(int(r*cos(t)+r*sin(t)+1)*r,r,0,2*cos(t),t,-pi/2,pi/2)syms t rs=int(r*cos(t)+r*sin(t)+1)*r,r,0,2*cos(t)q=int('s',t,-pi/2,pi/2)clcsyms t rs=int(r*cos(t)+r*sin(t)+1)*r,r,

29、0,2*cos(t)q=int(s,t,-pi/2,pi/2)clclcsyms xezplot('x2*sin(x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2);f=inline('x2*sin(x2-x-2)','x');x,f=fminsearch(f,-0.7);ff=inline('-x2*sin(x2-x-2)','x');x,f=fminbnd(ff,-2,2)syms xezplot('x2*sin(x2-x-2)',

30、-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2)f=inline('x2*sin(x2-x-2)','x')x,f=fminsearch(f,-0.7);ff=inline('-x2*sin(x2-x-2)','x');x,f=fminbnd(ff,-2,2)clcsyms xezplot('x2*sin(x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2)syms xezplot('x2*sin(

31、x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2)syms xezplot('x2*sin(x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2)syms xezplot('x2*sin(x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2)clcsyms xf=x2*sin(x2-x-2ezplot('x2*sin(x2-x-2)',-2,2);x,f0=

32、fminbnd('x2*sin(x2-x-2)',-2,2)x1,f1=fminsearch('-f',2.24)syms xf=x2*sin(x2-x-2)ezplot('x2*sin(x2-x-2)',-2,2);x,f0=fminbnd('x2*sin(x2-x-2)',-2,2)x1,f1=fminsearch('-f',2.24)syms xf=x2*sin(x2-x-2)ezplot('x2*sin(x2-x-2)',-2,2);x,f0=fminbnd('x2*sin(x2-x

33、-2)',-2,2)x1,f1=fminsearch(-f,2.24)syms xf=x2*sin(x2-x-2)ezplot('x2*sin(x2-x-2)',-2,2);x,f0=fminbnd('x2*sin(x2-x-2)',-2,2)x1,f1=fminsearch(-f,-1.554)clcsyms xezplot('x2*sin(x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2)x1,f1=fminsearch('-x2*sin(x2-x-2)'

34、,-1.554)x2,f2=fminsearch('-x2*sin(x2-x-2)',-0.754)x3,f3=fminsearch('-x2*sin(x2-x-2)',0)x4,f4=fminsearch('-x2*sin(x2-x-2)',1.62)clcsyms xezplot('x2*sin(x2-x-2)',-2,2);x,f=fminbnd('x2*sin(x2-x-2)',-2,2)x1,f1=fminsearch('-x2*sin(x2-x-2)',-1.554)x2,f2=fmin

35、search('x2*sin(x2-x-2)',-0.754)x3,f3=fminsearch('-x2*sin(x2-x-2)',0)x4,f4=fminsearch('x2*sin(x2-x-2)',1.62)clcclearfun=inline('x(1)4+x(2)2-4*x(1)*x(2)+4*x(1)+x(2)-9');x,g=fminsearch(fun,-1,-1)clcclearclcsyms z r xz=linspace(0,2,1000)r=sqrt(1+(z-1).2)x=rcylinder(r)x,r,

36、z=cylinder(r)syms z r xz=linspace(0,2,1000)r=sqrt(1+(z-1).2)x=rx,r,z=cylinder(r)syms z r xz=linspace(0,2,1000)r=sqrt(1+(z-1).2)x=rcylinder(r)syms z r xz=linspace(0,2,1000)r=sqrt(1+(z-1).2)x=rcylinder(r,'r')clcsyms x y z tx1=4*cos(t);y1=4*sin(t);z1=2*t;S1=jacobian(x1,y1,z1,t);t=pi/2;x0=4*cos(

37、t);y0=4*sin(t);z0=2*t;s0=subs(S1);syms tF=-x;y;z+x0;y0;z0+s0*t,G=x-x0;y-y0;z-z0*s0syms x y z tx1=4*cos(t);y1=4*sin(t);z1=2*t;S1=jacobian(x1,y1,z1,t);t=pi/2;x0=4*cos(t);y0=4*sin(t);z0=2*t;s0=subs(S1);syms tF=-x;y;z+x0;y0;z0+s0*tclcsyms x y z tx1=4*cos(t);y1=4*sin(t);z1=2*t;S1=jacobian(x1,y1,z1,t);t=p

38、i/2;x0=4*cos(t);y0=4*sin(t);z0=2*t;s0=subs(S1);syms tF=-x;y;z+x0;y0;z0+s0*tG=x-x0,y-y0,z-z0*s0p=x2*sin(x2-x-2)p(-2)clcf(-2)x(2)x5,f5=fminsearch('-x2*sin(x2-x-2)',-2)syms t y x zf=x2+2*y2+3*z2-36;x0=1;y0=2;z0=3w=x,y,z;s1=jacobian(f,w);v1=subs(s1,x,x0);z2=subs(v1,y,y0);n=subs(z2,z,z0);f=x-x0,y

39、-y0,z-z0*n',G=-x;y;z+x0;y0;z0+n'.*tsyms t y x zf=x2+2*y2+3*z2-36;x0=1;y0=2;z0=3w=x,y,z;s1=jacobian(f,w);v1=subs(s1,x,x0);z2=subs(v1,y,y0);n=subs(z2,z,z0);f=x-x0,y-y0,z-z0*n'G=-x,y,z+x0,y0,z0+n'.*tsyms t y x zf=x2+2*y2+3*z2-36;x0=1;y0=2;z0=3;w=x,y,z;s1=jacobian(f,w);v1=subs(s1,x,x0);z

40、2=subs(v1,y,y0);n=subs(z2,z,z0);f=x-x0,y-y0,z-z0*n'G=-x,y,z+x0,y0,z0+n'.*tclcsyms t y x zf=x2+2*y2+3*z2-36;x0=1;y0=2;z0=3;w=x,y,z;s1=jacobian(f,w);v1=subs(s1,x,x0);z2=subs(v1,y,y0);n=subs(z2,z,z0);f=x-x0,y-y0,z-z0*n'G=-x,y,z+x0,y0,z0+n'.*tsyms t y x zf=x2+2*y2+3*z2-36;x0=1;y0=2;z0=3;

41、w=x,y,z;s1=jacobian(f,w);v1=subs(s1,x,x0);z2=subs(v1,y,y0);n=subs(z2,z,z0);f=x-x0,y-y0,z-z0*n'G=-x;y;z+x0;y0;z0+n'.*tclcclearsyms xf=sin(x)2;t1=taylor(f,4,x)t2=taylor(f,8,x)t3=taylor(f,12,x)t4=taylor(f,16,x)clearsyms xf=sin(x)2;t1=taylor(f,4,x)t2=taylor(f,8,x)t3=taylor(f,12,x)t4=taylor(f,16,

42、x)CLCclcsyms x y z t R Kx1=R*cos(t);y1=R*sin(t);z1=K*t;S1=jacobian(x1,y1,z1,t);t=pi/2;x0=R*cos(t);y0=R*sin(t);z0=K*t;s0=subs(S1);syms tF=-x;y;z+x0;y0;z0+s0*t,G=x-x0;y-y0;z-z0*s0syms x y z t R Kx1=R*cos(t);y1=R*sin(t);z1=K*t;S1=jacobian(x1,y1,z1,t);t=pi/2;x0=R*cos(t);y0=R*sin(t);z0=K*t;s0=subs(S1);sy

43、ms tF=-x;y;z+x0;y0;z0+s0*t,G=x-x0,y-y0,z-z0*s0clctaylortoolclearx=-6:0.01:6;f=sin(x).2;t1=x.2;t2=(2.*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f,x,t1,''

44、;,x,t2,'%',x,t3,'*',x,t4,'&')clearx=-6:0.01:6;f=sin(x).2;t1=x.2;t2=(2.*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f)clearx=-6:0.01:6

45、;f=sin(x).2;t1=x.2;t2=(2.*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,t1)clearx=-6:0.01:6;f=sin(x).2;t1=x.2;t2=(2.*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8

46、/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,t2)clcclearx=-6:0.01:6;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467

47、775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,t2)clearx=-6:0.01:6;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f)clea

48、rx=-pi:0.01:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f)clearx=-pi:0.01:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10

49、)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,t1)clearx=-pi:0.01:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (

50、2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f,x,t1,'')clearx=-pi:0.01:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/4

51、5 - x.4/3 + x.2;plot(x,f,x,t1,'',x,t2,'*')clearx=-pi:0.1:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f,x,t1,''

52、,x,t2,'*')clearx=-pi:0.1:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f,x,t1,'',x,t2,'*',x,t3,'#',x,t4,

53、'')clearx=-pi:0.1:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f,x,t1,'',x,t2,'*',x,t3,'#')clearx=-pi:0

54、.1:pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f,x,t1,'',x,t2,'*')clearx=-10*pi:0.1:10*pi;f=sin(x).2;t1=x.2;t2=(2*x.6)/45 - x.4/3 + x.2;t3=(2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;t4=(4.*x.14)/42567525 - (2.*x.12)/467775 + (2.*x.10)/14175 - x.8/315 + (2.*x.6)/45 - x.4/3 + x.2;plot(x,f,x,t1,'',x,t2,'*',x,t3,'#',x,t4