符号计算基础与符号微积分

练习十符号计算基础与符号微积分1.已知x=6，y=5，利用符号表达式求yxxz31。提示：定义符号常数)'5(')'6('symysymx，。x=sym('6');y=sym('5');z=(x+1)/(sqrt(3+x)-sqrt(y))2.分解因式。(1)44yx(2)5135（1）symsxy;factor(x^4-y^4)（2）factor(sym('5135'))3.化简表达式。(1)2121sincoscossin(2)123842xxx（1）symsbeta1beta2z=sin(beta1)*cos(beta2)-cos(beta1)*sin(beta2);simplify(z)（2）x=sym('x');z=(4*x^2+8*x+3)/(2*x+1);simplify(z)4.已知ihgfedcbaAPP，，10101000110000101021完成下列运算：(1)B=APP21。(2)B的逆矩阵并验证结果。(3)包括B矩阵主对角线元素的下三角阵。(4)B的行列式值。P1=[0,1,0;1,0,0;0,0,1];P2=[1,0,0;0,1,0;1,0,1];A=sym('[a,b,c;d,e,f;g,h,i]');B=P1*P2*A%(1)inv(B)%(2)tril(B)%(3)det(B)%(4)5.用符号方法求下列极限或导数。(1)xeexxxx3tansin0sin)1(2)1(lim(2)1arccoslim1xxx(3)xxy)2cos(1，求yy、。(4)已知xxttaAxlncos3，分别dxdtAddtAddx222dA、、(5)已知xyyxexxyxf22)2(),(2，求201xyyfxxy，、%(1)x=sym('x');t=sym('t');g1=(x*(exp(sin(x))+1)-2*(exp(tan(x))-1))/sin(x)^3;limit(g1,0)%(2)g2=(sqrt(pi)-sqrt(acos(x)))/sqrt(x+1);limit(g2,x,-1,'right')%(3)y=(1-cos(2*x))/x;diff(y)diff(y,2)%(4)A=sym('[a^x,t^3;t*cos(x),log(x)]');diff(A,x)diff(A,t,2)diff(A,x,t)%(5)y=sym('y');f=(x^2-2*x)*exp(-x^2-y^2-x*y);dfx=diff(f,x)subs(dfx,[x,y],[0,1])dfxy=diff(f,x,y)subs(dfxy,[x,y],[0,1])6.用符号方法求下列积分。(1)841xxdx(2)221)(arcsinxxdx(3)04211dxxx(4)2ln02)1(dxeexx%(1)x=sym('x');int(1/(1+x^4+x^8))%(2)int(1/(asin(x)^2*sqrt(1-x^2)))%(3)int((x^2+1)/(x^4+1),x,0,inf)%(4)int(exp(x)*(1+exp(x))^2,x,0,log(2))