6 MATLAB的符号计算答案.docx

1、6 MATLAB的符号计算答案%红色为程序运行结果%PPT12页练习syms x;f=cos(x)+sqrt(-(sin(x)2);y1=simplify(f)y2=simple(f) y1 = cos(x)+(-1+cos(x)2)(1/2)y2 = cos(x)+i*sin(x)%PPT13页例题syms a x;f=a*sin(x)+5;f1=subs(f,a,x,2,pi/3)f2=subs(f,sin(x),y)f1 = 6.7321f2 = a*y+5%PPT18页求极限1syms x;f=(1+4*x)(1/x);limit(f)ans = exp(4)2syms x;f=(ex

2、p(x)-1)/x;limit(f)ans = 13syms x;f=2*sin(x)/(x3+3*x);limit(f)ans = 2/34syms x;f=(sqrt(5*x-4)-sqrt(x)/(x-1);limit(f,x,1)ans = 25syms x;f=(1-2/x)(2*x);limit(f,x,inf)ans = exp(-4)6syms x;f=(sin(1/x)+cos(1/x)x;limit(f,x,inf)ans = exp(1)%PPT22参数方程例题syms t;x=log(cos(t);y=cos(t)-t*sin(t);y1=diff(y,t)/diff(

3、x,t)y2=diff(y,t,2)/diff(x,t,2)t=pi/3;eval(y2)y1 = -(-2*sin(t)-t*cos(t)/sin(t)*cos(t)y2 = (-3*cos(t)+t*sin(t)/(-1-sin(t)2/cos(t)2)ans = 0.1483%PPT23页求导部分1syms x;f=x10+10x+1/log10(x);y=diff(f)y = 10*x9+10x*log(10)-1/log(x)2*log(10)/x2syms x;f=log(2-x2);diff(f,2)ans = -2/(2-x2)-4*x2/(2-x2)23syms x y;f=

4、exp(2*x)*(x+y2+2*y);y1=diff(f,x)y2=diff(f,y)y1 = 2*exp(2*x)*(x+y2+2*y)+exp(2*x)y2 = exp(2*x)*(2*y+2)4syms x y;f=(cos(2*x+y)2;y1=diff(f,x,2)y2=diff(f,y,2)y1 = 8*sin(2*x+y)2-8*cos(2*x+y)2y2 = 2*sin(2*x+y)2-2*cos(2*x+y)25syms x y;s=x2*sin(y);y1=diff(f,x)y2=diff(y1,y)y1 = -4*cos(2*x+y)*sin(2*x+y)y2 = 4*

5、sin(2*x+y)2-4*cos(2*x+y)2%PPT26页求不定积分1syms x;f=x2/sqrt(2-x2);y=int(f)y = -1/2*x*(2-x2)(1/2)+asin(1/2*2(1/2)*x)2syms x;f=sin(2*x)*sin(3*x);y=int(f)y = 1/2*sin(x)-1/10*sin(5*x)3syms a b x;f=1/(x*(log(x)+a+sqrt(log(x)+b);y=int(f)y = 1/2*log(log(x)2+2*log(x)*a+a2-log(x)-b)+1/(-4*b-1+4*a)(1/2)*atan(2*log

6、(x)+2*a-1)/(-4*b-1+4*a)(1/2)-1/2*log(log(x)+a-(log(x)+b)(1/2)-1/(-4*b-1+4*a)(1/2)*atan(2*(log(x)+b)(1/2)-1)/(-4*b-1+4*a)(1/2)+1/2*log(log(x)+a+(log(x)+b)(1/2)-1/(-4*b-1+4*a)(1/2)*atan(1+2*(log(x)+b)(1/2)/(-4*b-1+4*a)(1/2)4syms x;f=sin(x) x3;x*exp(x) tan(x);y=int(f)y = -cos(x), 1/4*x4 x*exp(x)-exp(x)

7、, -log(cos(x)%PPT28页求一元定积分1syms x;f=exp(-x2);int(f,x,0,1)ans = 1/2*erf(1)*pi(1/2)2syms t;f=(t2+4)/(t2+2);int(f,t,0,2)ans = 2+2(1/2)*atan(2(1/2)3syms x;f=sqrt(sin(x)3-(sin(x)5);int(f,x,0,pi)ans = 1/5*2(1/2)*8(1/2)4syms x;f=1/(1+8*(sin(x)2);int(f,x,0,pi/6)ans = -1/3*atan(cot(5/12*pi)/(2*2(1/2)-3)+1/3*

8、atan(cot(5/12*pi)/(3+2*2(1/2)5syms x t;f=exp(-5*x)*sin(3*x+pi/3);p=subs(f,x,t+x);y=f*p;int(y,0,t)ans = 1/17680*(100*sin(t)*3(1/2)-7800*sin(t)*cos(t)2+402*cos(t)+195*sin(t)+1700*sin(t)3*cos(t)2*3(1/2)-41600*cos(t)9+93600*cos(t)7+11310*cos(t)3*3(1/2)-76300*sin(t)*3(1/2)*cos(t)4+145600*sin(t)*3(1/2)*co

9、s(t)6+10875*sin(t)*cos(t)2*3(1/2)+10920*sin(t)2*3(1/2)*cos(t)3-31200*sin(t)2*3(1/2)*cos(t)5-1170*sin(t)2*3(1/2)*cos(t)+24960*sin(t)2*cos(t)7*3(1/2)+1300*exp(t)10*sin(t)*cos(t)2*3(1/2)+41600*cos(t)7*sin(t)2-52000*sin(t)2*cos(t)5-780*exp(t)10*sin(t)*cos(t)2-585*exp(t)10*cos(t)*3(1/2)-325*exp(t)10*sin(

10、t)*3(1/2)+780*exp(t)10*cos(t)3*3(1/2)-585*cos(t)*3(1/2)-675*cos(t)*sin(t)2+16500*cos(t)3*sin(t)2-71900*cos(t)5+18289*cos(t)3+46800*cos(t)4*sin(t)-24960*3(1/2)*cos(t)9-87360*cos(t)6*sin(t)+49920*cos(t)8*sin(t)+56160*3(1/2)*cos(t)7-42120*3(1/2)*cos(t)5-425*sin(t)3*3(1/2)-83200*sin(t)*cos(t)8*3(1/2)+48

11、36*exp(t)10*cos(t)3-3627*exp(t)10*cos(t)+195*exp(t)10*sin(t)/exp(t)15%PPT31页多重积分运算1syms x y;f=x2*exp(-y2);int(int(f,x,0,y),y,0,1)ans = -1/3*exp(-1)+1/62syms x y; iy=int(sqrt(1-x2),y,-sqrt(1-x2),sqrt(1-x2);int(iy,x,-1,1)ans = 8/3%PPT34页多重积分运算1syms t;t=0:0.1:10;y=exp(-0.8.*t.*abs(sin(t);s1=trapz(t,y)f

12、f=inline(exp(-0.8.*t.*abs(sin(t);s2=quad(ff,0,10)s1 = 2.6576s2 = 2.65972syms x;x=exp(1):0.1:6;y=x.2.*log(x);s1=trapz(x,y)ff=inline(x.2.*log(x);s2=quad(ff,exp(1),6)s1 = 95.3790s2 = 100.54323syms x;x=0:pi/12:pi;y=sqrt(sin(x)-(sin(x).3);ff=inline(sqrt(sin(x)-(sin(x).3);s1=trapz(x,y)s2=quad(ff,0,pi)s1 =

13、 1.2661s2 = 1.33334syms x;x=-1:0.1:1;y=exp(-x.2);ff=inline(exp(-x.2);s1=trapz(x,y)s2=quad(ff,-1,1)s1 = 1.4924s2 = 1.4936%PPT35页多重积分运算1syms x y;ff=inline(x.2+y);q=dblquad(ff,0,1,0,1)q = 0.83332syms x y;ff=inline(y.2./x.2);q=dblquad(ff,1/2,2,1,2)q = 3.50003syms r theda;ff=inline(sqrt(1+r.*sin(theda);q

14、=dblquad(ff,0,1,0,pi)q = 3.5909%PPT39页多重积分运算1、syms x n;f1=(1+x/n)n;f2=(-1)n*xn/n;f3=sin(x*y);s1=limit(f1,n,inf)s2=symsum(f2,1,inf)s3=diff(f3,x,2)s1 = exp(x)s2 = sum(-1)n*xn/n,x = 1 . Inf)s3 = -sin(x*y)*y22syms x;f=sin(x);s=taylor(f,6,x,0)s = x-1/6*x3+1/120*x53（1）syms n k;f=1/(5*k-4)*(5*k+1);s1=symsu

15、m(f,k,1,n)s2=symsum(f,k,1,inf)s1 = -1/5/(5*n+1)+1/5s2 = 1/53（2）syms n k;f=1/2k+1/3k;s1=symsum(f,k,1,n)s2=symsum(f,k,1,inf)s1 = -2*(1/2)(n+1)-3/2*(1/3)(n+1)+3/2s2 = 3/24（1）syms n k;f=1/(2*k)2-1);f1=symsum(f,k,1,n);s=limit(f1,n,inf)s = 1/24（2）syms n k;f=1/(n2+k*pi);f1=symsum(f,k,1,n);s=limit(n*f1,n,in

16、f)s = 1%PPT43页例题ff=inline(x(1)4+sin(x(2)-cos(x(3);x0=0 5 4;x,fval=fminsearch(ff,x0)x = -0.0021 4.7124 6.2832fval = -2.0000%PPT45页练习x1=fzero(x4-4*x-5,-5) %第（1）题 x2=fzero(sin(3*x),2) %第（2）题 x3=fzero(sin(x)-log(x+0.1),1) %第（3）题x1 = -1x2 = 2.0944 x3 = NaN%PPT45页练习（1）syms x a b;s=x2-a*x-4*b;solve(s)ans =

17、 1/2*a+1/2*(a2+16*b)(1/2) 1/2*a-1/2*(a2+16*b)(1/2)（2）solve(sym(x9-x8+1)ans = 1.1228174396026853653525590840144+.28363052586617358353928597350912*i .60944290027631923574927798035197+.80967283242662774065903710738338*i -.85784190205533577358632528477576e-1+.95128761278822288069698079288831*i -.6856764

18、8985647952059348937828781+.62718337618433236630566609958131*i -.92159931963398300629943031520197 -.68567648985647952059348937828781-.62718337618433236630566609958131*i -.85784190205533577358632528477576e-1-.95128761278822288069698079288831*i .60944290027631923574927798035197-.80967283242662774065903

19、710738338*i 1.1228174396026853653525590840144-.28363052586617358353928597350912*i（3）solve(sym(x6-x2+2*x-3)ans = 1.1238932511762955476010811097327 .60804677070454177795683814517971+.88541124247455434577495883624571*i -.46586916707607665574895492689981+1.1941322239415680694023931300200*i -1.4082484584

20、332257920168475462925 -.46586916707607665574895492689981-1.1941322239415680694023931300200*i .60804677070454177795683814517971-.88541124247455434577495883624571*i%PPT50页练习（1）（2）x1=solve(x2+b*x+c=0) %第(1)题x2=solve(a*x2-b*x-6=0) %第(2)题x2 = 1/2/a*(b+(b2+24*a)(1/2) 1/2/a*(b-(b2+24*a)(1/2)（3）（4）x3,y3=sol

21、ve(x+y=1,x-11*y=5,x,y) %第（3）题 x4,y4=solve(x+3*y=1,x2+y2=1,x,y) %第（4）题x3 = 4/3 y3 = -1/3x4 = 1 -4/5y4 = 0 3/5%PPT52页练习1ff=inline(x(1)-x(2)2,x(2)-cos(x(1),x);f=fsolve(ff,1,2)f = 0.6417 0.80112ff=inline(sin(x(1)+x(2)2+log(x(3)-7,3*x(1)+x(2)2-x(3)3+1,x(1)+x(2)+x(3),x);f=fsolve(ff,1,1,1)f = -3.1420 2.905

22、1 0.2370%PPT57页练习s1=dsolve(Dy=x*sin(x)/cos(y),x) %第（1）题s2=dsolve(D2y+4*Dy+29*y=0,y(0)=0,Dy(0)=15,x) %第（2）题%第（3）题x,y,z=dsolve(Dx=2*x-3*y+3*z,Dy=4*x-5*y+3*z,Dz=4*x-4*y+2*z,t);x=simple(x)y=simple(y)z=simple(z)s1 = -asin(-sin(x)+x*cos(x)-C1)s2 = 3*exp(-2*x)*sin(5*x)x = C2*exp(t)2+C3/exp(t)y = C3*exp(-t)

23、+C2*exp(2*t)+exp(-2*t)*C1z = C2*exp(2*t)+exp(-2*t)*C1s4=dsolve(x*Dy=y*log(x*y)-y,x) %第（4）题s5=dsolve(Dv+2*t=0,v(1)=5,t) %第（5）题s6=dsolve(D2y-(a+b)*Dy+a*b*y=0) %第（6）题s7=dsolve(D2y=x*sin(x),y(0)=1/2,Dy(2)=0,x) %第（7）题s4 = exp(x/C1)/xs5 = -t2+6s6 = C1*exp(b*t)+C2*exp(a*t)s7 = -2*cos(x)-x*sin(x)+(-sin(2)+2*cos(2)*x+5/2%PPT61页练习1ezplot(sin(x),0,pi) 2ezplot(cos(t)3,(sin(t)3,0,2*pi)3ezplot(exp(x)+sin(x*y),-2,0.5,0,2)