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1、1.求下列函数极限（Findthelimitsofthefollowingfunctions）(1)symsxr;r=sin(x)/x;limit(r,x,0)ans=1(2)symsxr;r=(1+1/x)^x;limit(r,x,inf)ans=exp(1)(3)symsxra;r=(1+a/x)^x;limit(r,x,inf)ans=exp(a)(4)symsxr;r=(1+1/x)^x;limit(r,x,-inf)ans=exp(1)(5)symsxr;r=(1-cos(x))/(x^2)
2、;limit(r,x,0)ans=1/2(6)symsnr;r=n^(1/n);limit(r,n,inf)ans=1(7)symsxnr;r=(cos(sqrt(x)))^(n/x);limit(r,x,0,'right')ans=1/exp(n/2)2.求下列函数的导数或偏导数(Findthederivativesofthefollowingfunctions)(1)symsxabcfg;f=sqrt(a*x^2+b*x+c);g=sqrt(exp(x^2)+x*sin(x));a1=diff(f
3、,x)a2=diff(g,x)a1=(b+2*a*x)/(2*(a*x^2+b*x+c)^(1/2))a2=(sin(x)+2*x*exp(x^2)+x*cos(x))/(2*(exp(x^2)+x*sin(x))^(1/2))(2)symsxf;f=log(x^3);diff(f,x)ans=3/x(3)Findthe3rdderivativeoff(x).symsxf;f=x*exp(-x^2);diff(f,x,3)ans=(24*x^2)/exp(x^2)-6/exp(x^2)-(8*x^4)
4、/exp(x^2)(4))Findsymsxyf;f=x^3-2*x^2*y^2+3*y-5;diff(f,x,2)ans=6*x-4*y^2(5)Find.symsxyf;f=x^3-2*x^2*y^2+3*y-5;fx=diff(f,x);fxy=diff(fx,y)fxy=-8*x*y3.求下列函数的不定积分或定积分（Findindefiniteintegralsordefiniteintegralsofthefunctions）(1)symsxs;s=sin(x)-2*cos(3*x)+1/x
5、+exp(-x);int(s,x)ans=log(x)-(2*sin(3*x))/3-cos(x)-1/exp(x)(2)symsxs;s=exp(x)*sin(exp(x));int(s,x)ans=-cos(exp(x))(3)symsxs;s=x^2/(sqrt(x^6)+4);int(s,x)Warning:Explicitintegralcouldnotbefound.ans=int(x^2/((x^6)^(1/2)+4),x)(4)symsxs;s=cos(3*x)*cos(5*x);in
6、t(s,x)ans=sin(2*x)/4+sin(8*x)/16(5)symsxsa;s=(sqrt(x^2-a^2))/x;int(s,x)ans=(x^2-a^2)^(1/2)-log(((-a^2)^(1/2)+(x^2-a^2)^(1/2))/x)*(-a^2)^(1/2)(6)symsxsab;s=exp(a*x)*sin(b*x);int(s,x)ans=-(exp(a*x)*(b*cos(b*x)-a*sin(b*x)))/(a^2+b^2)(7)symsxs;s=sqrt(sin(x)
7、-(sin(x))^3);int(s,x,0,pi)Warning:Explicitintegralcouldnotbefound.ans=int((sin(x)-sin(x)^3)^(1/2),x=0..pi)(8)symsxs;s=1/(x^2);int(s,x,1,inf)ans=14.解下列方程（Solvetheequations.）(1)symsx;solve(sqrt(1-x^2)-x,x)ans=2^(1/2)/2(2)symsxyz;s=solve(x+y+z-10,x-y+z,2*x
8、-y-z+4,x,y,z)s.x,s.y,s.zs=x:[1x1sym]y:[1x1sym]z:[1x1sym]ans=2ans=5ans=3(3)symsxyz;s=solve(x^2+4*x*y+z,x+3*y*z-3,y+sin(z),x,y,z)s.x,s.y,s.zs=x:[1x1sym]y:[1x1sym]z:[1x1sym]ans=-6.4840528860501102693511549985753ans=-0.07199575840308
