Câu 1 >> syms x y z >> y=z^2 x^2; >> ezsurf(x,y,z) Câu 2 >> syms x y >> u=sin(x*y); >> f=exp(u^2); >> diff(f,1,x) ans = 2*y*exp(sin(x*y)^2)*cos(x*y)*sin(x*y) >> diff(f,1,y) ans = 2*x*exp(sin(x*y)^2)*c[.]
Câu 1: >> syms x y z >> y=z^2-x^2; >> ezsurf(x,y,z) Câu 2: >> syms x y >> u=sin(x*y); >> f=exp(u^2); >> diff(f,1,x) ans = 2*y*exp(sin(x*y)^2)*cos(x*y)*sin(x*y) >> diff(f,1,y) ans = 2*x*exp(sin(x*y)^2)*cos(x*y)*sin(x*y) Câu 3: >> syms x y lamda dx dy >> f=2*x^2+12*x*y+y^2; >> g=x^2+4*y^2-25; >> L=f+lamda*g; >> [lamda0 x0 y0]=solve(diff(L,x),diff(L,y),g) lamda0 = 2 -17/4 -17/4 x0 = -3 -4 y0 = -2 -3/2 3/2 >> A=diff(L,2,x) A= 2*lamda + >> B=diff(diff(L,x),y) B= 12 >> C=diff(L,2,y) C= 8*lamda + >> dg=2*x*dx+8*y*dy; >> dx0=solve(dg,dx) dx0 = -(4*dy*y)/x >> d2L=A*dx^2+2*B*dx*dy+C*dy^2; >> d2L=subs(d2L,dx,dx0) d2L = dy^2*(8*lamda + 2) - (96*dy^2*y)/x + (16*dy^2*y^2*(2*lamda + 4))/x^2 >> for i=1:length(x0) subs(d2L,[x y lamda],[x0(i) y0(i) lamda0(i)]) end ans = (1250*dy^2)/9 ans = (1250*dy^2)/9 ans = -(625*dy^2)/8 ans = -(625*dy^2)/8 >> syms t >> x=cos(t);y=sin(t); >> f=2*x^2+12*x*y+y^2; >> ezplot3(x,y,f,[0,2*pi]) >> hold on >> syms x y >> f=2*x^2+12*x*y+y^2; >> for i=1:length(x0) f0(i)=subs(f,[x,y],[x0(i) y0(i)]); end >> f0 f0 = [ -50, -50, 425/4, 425/4] >> for i=1:length(x0) plot3(x0(i),y0(i),f0(i),'marker','+') hold on end Câu 4: >> syms x y z real >> P=2*x+y; >> Q=2*y+z; >> R=2*z+x; >> f=x+y+z-3; >> n=[diff(f,'x'),diff(f,'y'),diff(f,'z')]; >> n=n/sqrt(diff(f,'x')^2+diff(f,'y')^2+diff(f,'z')^2); >> p=(diff(R,'y')-diff(Q,'z')*n(1,1)); >> q=(diff(P,'z')-diff(R,'x')*n(1,2)); >> r=(diff(Q,'x')-diff(P,'y')*n(1,3)); >> z=3-y-x; >> f=(eval(p)+eval(q)+eval(r))*sqrt(1+diff(z,'x')^2+diff(z,'y')^2); >> syms r phi real >> x=r*cos(phi);y=r*sin(phi); >> f=eval(f); >> S=int(int(f*r,'r',0,1),'phi',0,2*pi); >> S=double(S) S= -9.4248 >> t=linspace(0,2*pi,50); >> x=cos(t); >> y=sin(t); >> z=3-x-y; >> plot3(x,y,z,'color','b') >> xlabel('truc x') >> ylabel('truc y') >> zlabel('truc z') Câu 5: >> syms n >> symsum(1/((3*n+1)*(n-2)),3,inf) ans = 117/196 - (pi*3^(1/2))/42 - (3*log(3))/14