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3101301218 邱振涛 练习三：符号运算 用MATLAB符号运算做下列各题 求极限，， syms x h L=limit((log(x+h)-log(x))/h,h,0) L =1/x syms a n M=limit((1-a/n)^n,n,inf) M =exp(-a) syms x P=limit((exp(1)-(1+x)^(1/x))/x,x,0) P =NaN 求和，， syms k n S1=symsum(k^2,k,1,n) S1 =1/3*(n+1)^3-1/2*(n+1)^2+1/6*n+1/6 syms k n S2=symsum(1/k^2,k,1,inf) S2 =1/6*pi^2 syms x n S3=symsum(x^n/(n*(n-1)),n,2,inf) S3 =-(x-1)*log(1-x)+x 3、求导数并化简、求偏导数 syms x a diff(log(x+sqrt(a^2+x^2)),x,5) =(105/(a^2+x^2)^(9/2)*x^5-150/(a^2+x^2)^(7/2)*x^3+45/(a^2+x^2)^(5/2)*x)/(x+(a^2+x^2)^(1/2))-5*(-15/(a^2+x^2)^(7/2)*x^4+18/(a^2+x^2)^(5/2)*x^2-3/(a^2+x^2)^(3/2))/(x+(a^2+x^2)^(1/2))^2*(1+1/(a^2+x^2)^(1/2)*x)+20*(3/(a^2+x^2)^(5/2)*x^3-3/(a^2+x^2)^(3/2)*x)/(x+(a^2+x^2)^(1/2))^3*(1+1/(a^2+x^2)^(1/2)*x)^2-10*(3/(a^2+x^2)^(5/2)*x^3-3/(a^2+x^2)^(3/2)*x)/(x+(a^2+x^2)^(1/2))^2*(-1/(a^2+x^2)^(3/2)*x^2+1/(a^2+x^2)^(1/2))-60*(-1/(a^2+x^2)^(3/2)*x^2+1/(a^2+x^2)^(1/2))/(x+(a^2+x^2)^(1/2))^4*(1+1/(a^2+x^2)^(1/2)*x)^3+30*(-1/(a^2+x^2)^(3/2)*x^2+1/(a^2+x^2)^(1/2))^2/(x+(a^2+x^2)^(1/2))^3*(1+1/(a^2+x^2)^(1/2)*x)+24*(1+1/(a^2+x^2)^(1/2)*x)^5/(x+(a^2+x^2)^(1/2))^5 化简得 =3*(3*a^4-24*a^2*x^2+8*x^4)/(a^2+x^2)^(9/2) syms x y z f f1 f2 f3 f4 f=diff(sin(x^2*y*z),x,2) f1=diff(f,y,1) f2=subs(f1,x,1) f3=subs(f2,y,1) f4=subs(f3,z,3) = 88.2784 4、求不定积分 ， syms x i i=int((x^2+1)/(x^2-2*x+2)^2,x) i =3/2*atan(x-1)+1/4*(2*x-6)/(x^2-2*x+2) syms a b x j j=int(1/(x*(sqrt(a+log(x))+sqrt(b+log(x)))),x) j=-2/3/(-b+a)*(b+log(x))^(3/2)+2/3/(-b+a)*(a+log(x))^(3/2) 5、求定积分，含参积分 syms x I I=int(exp(-x^2),0,inf) I =1/2*pi^(1/2) syms x y f f=int((x-y)^3*sin(x+2*x),y) subs(f,x)-subs(f,-x) I(x)= -1/4*(x-y)^4*sin(3*x)-1/4*(-x-y)^4*sin(3*x) 6、试求正弦函数的次麦克劳林展开式，在同一幅图上画出正弦函数以及它的次麦克劳林多项式的图像，观察逼近情况。 7、试求方程或方程组的解： (1) ; (2) syms x x=solve(4*x^4-2*x^2-3*x+1) x = 1/6*(37+9*17^(1/2))^(1/3)-1/3/(37+9*17^(1/2))^(1/3)-1/3 -1/12*(37+9*17^(1/2))^(1/3)+1/6/(37+9*17^(1/2))^(1/3)-1/3+1/2