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1、实验十符号计算基础与符号微积分1、x=sym('6');y=sym('5');z=(x+1)/(sqrt(x+3)-sqrt(y))z=-7/(5^(1/2)-3)2、（1）symsxy;factor(x^4-y^4)ans=(x-y)*(x+y)*(x^2+y^2)（2）factor(sym('5135'))ans=5*13*793、symsbeta1beta2x;f1=sin(beta1)*cos(beta2)-cos(beta1)*sin(beta2);f2=(4*x^2+8*x+3)/(2*x+1);simplify(f1)simplify(f2)ans=sin(b
2、eta1-beta2)ans=2*x+34、（1）p1=[010;100;001];p2=[100;010;101];A=sym('[abc;def;ghi]');B=p1*p2*AB=[d,e,f][a,b,c][a+g,b+h,c+i]（2）simplify(inv(B)*B)ans=[1,0,0][0,1,0][0,0,1]（3）tril(B)ans=[d,0,0][a,b,0][a+g,b+h,c+i]（4）det(B)ans=a*f*h+b*d*i-a*e*i-b*f*g-c*d*h+c*e*g5、（1）symsx;f1=(x*(exp(sin(x))+1)-2*
3、(exp(tan(x))-1))/sin(x)^3limit(f1)ans=-1/2（2）f2=(sqrt(pi)-sqrt(acos(x)))/sqrt(x+1);limit(f2,x,-1,'right')ans=-Inf（3）y=(1-cos(2*x))/x;y1=diff(y)y2=diff(y,2)y1=(2*sin(2*x))/x+(cos(2*x)-1)/x^2y2=(4*cos(2*x))/x-(4*sin(2*x))/x^2-(2*(cos(2*x)-1))/x^3（4）symsaxt;A=[a^xt^3;t*cos(x)log(x)];Ax=diff(A
4、,x,1)At=diff(A,t,2)Atx=diff(diff(A,t),x)Ax=[a^x*log(a),0][-t*sin(x),1/x]At=[0,6*t][0,0]Atx=[0,0][-sin(x),0]（5）symsxy;f=(x^2-2*x)*exp(-x^2-y^2-x*y);yx=-diff(f,x)/diff(f,y)dyx=diff(diff(f,y),x);x=sym('0');y=sym('1');eval(dyx)yx=-(exp(x^2+x*y+y^2)*(exp(-x^2-x*y-y^2)*(2*x-2)+exp(-x^2-x*y-y^2)*
5、(-x^2+2*x)*(2*x+y)))/((-x^2+2*x)*(x+2*y))ans=4*exp(-1)6、symsx;f1=1/(1+x^4+x^8);f2=1/(asin(x))^2/sqrt(1-x^2);f3=(x^2+1)/(x^4+1);f4=exp(x)*(1+exp(x))^2;F1=int(f1)F2=int(f2)F3=int(f3,0,inf)F4=int(f4,0,log(2))F1=-(3^(1/2)*(atan((2*3^(1/2)*x)/(3*((2*x^2)/3-2/3)))-atanh((2*3^(1/2)*x)/(3*((2*x^2)
6、/3+2/3)))))/6F2=-1/asin(x)F3=(pi*2^(1/2))/2F4=(exp(6243314768165359/9007199254740992)*(3*exp(6243314768165359/9007199254740992)+exp(6243314768165359/4503599627370496)+3))/3-7/3
