ĐỀ TÀI 2 Câu 1 Code như sau function detai2cau1 syms u v a = input(''''Nhap a=''''); b = input(''''Nhap b=''''); c = input(''''Nhap c=''''); x = a*sin(u)*cos(v); y = b*sin(u)*sin(v); z= c*cos(u); ezsurf(x,y,z,[0,pi,0,2[.]
ĐỀ TÀI Câu 1: Code sau: function detai2cau1 syms u v a = input('Nhap a='); b = input('Nhap b='); c = input('Nhap c='); x = a*sin(u)*cos(v); y = b*sin(u)*sin(v); z= c*cos(u); ezsurf(x,y,z,[0,pi,0,2*pi]); xlabel('x'); ylabel('y'); zlabel('z'); title('Mat elippsoid'); end ví dụ a=4, b=5,c=7,Kết sau: Câu 2: syms x y z real >> f=x*y-sinh(x+y-z^2) f = sinh(z^2 - x - y) + x*y >> z=solve(f,z) z = (x + y - asinh(x*y))^(1/2) -(x + y - asinh(x*y))^(1/2) >> KQ=subs(diff(z,x,2),[x y],[0 1]) KQ = 0 >> % Vì đạo hàm hàm z lần theo biến x =0 nên đạo hàm z''xx (0,1)=0 Câu 3: syms x y dx dy lamda real phi=x^2+y^2-1; dphi=diff(phi,x)*dx+diff(phi,y)*dy; L=x^2+2*y^2+lamda*(x^2+y^2-1); d2L = diff(L,x,2)*(dx)^2+2*dx*dy*diff(diff(L,x),y)+diff(L,y,2)*(dy)^2; >> >> [x0 y0 lamda0] = solve(diff(L,x),diff(L,y),phi,x,y,lamda) x0 = 0 -1 y0 = -1 lamda0 = -1 -2 -2 -1 >> z0=[0;0;0;0]; >> % gia tri dphi tuong ung tai cap diem(x0,y0) lan luot la >> for i = 1:length(x0) disp(subs(dphi,[x y],[x0(i) y0(i)])); z0(i)=subs(x^2+2*y^2,[x y],[x0(i) y0(i)]); end; 2*dx 2*dy -2*dy -2*dx >> % gia tri z0 tuong ung x0,y0 la >> disp(z0) 2 >> syms t ezplot3(cos(t),sin(t),cos(t)^2+2*sin(t)^2,[0 2*pi]); title('do thi giao tuyen cua z=x^2+2y^2 x^2+y^2=1'); hold on; %TH1 >> dx1=solve('2*dx') dx1 = >> subs(subs(d2L,dx,dx1),[x y lamda],[x0(1) y0(1) lamda0(1)]) ans = 2*dy^2 >> % ham dat cuc tieu tai diem(1,0,1) >> plot3(1,0,1,'marker','*'); text(1,0,1,'CT(1,0,1)'); %TH2 >> dy1=solve('2*dy') dy1 = >> subs(subs(d2L,dy,dy1),[x y lamda],[x0(2) y0(2) lamda0(2)]) ans = -2*dx^2 >> %ham dat cuc dai tai diem(0,1,2) >> plot3(0,1,2,'marker','*'); text(0,1,2,'CD(0,1,2)'); % TH3 >> dy2=solve('-2*dy') dy2 = >> subs(subs(d2L,dy,dy2),[x y lamda],[x0(3) y0(3) lamda0(3)]) ans = -2*dx^2 >> % ham dat cuc dai tai diem (0,-1,2) >> plot3(0,-1,2,'marker','*'); text(0,-1,2,'CD(0,-1,2)’); % TH4 >> dx2=solve('-2*dx') dx2 = >> subs(subs(d2L,dx,dx2),[x y lamda],[x0(4) y0(4) lamda0(4)]) ans = 2*dy^2 >> %ham dat cuc tieu tai(-1,0,1) >> plot3(-1,0,1,'marker','*'); text(-1,0,1,'CT(-1,0,1)'); Đồ thị đánh dấu điểm: Câu >> syms x y >> ezplot(x,x,[0 1]); >> hold on; >> ezplot(x,2-x,[1 2]); >> hold on; >> ezplot(x,0*x,[0 2]); >> hold on; >> y1=x; y2=0*x+0; x1=linspace(0,1); x2=linspace(1,0); Y1=subs(y1,x,x1); Y2=subs(y2,x,x2); fill([x1 x2],[Y1 Y2],'r'); >> hold on >> y1=2-x; y2=0*x+0; x1=linspace(1,2); x2=linspace(2,1); Y1=subs(y1,x,x1); Y2=subs(y2,x,x2); fill([x1 x2],[Y1 Y2],'r'); hold on; >> title('Mien D') >> I1=int(int(x*y+2*y,y,0,x),x,0,1) I1 = 11/24 >> I2=int(int(x*y+2*y,y,0,2-x),x,1,2) I2 = 13/24 >> I=I1+I2 I= Tô màu miền D, tích phân lấy cận chia miền D1, D2: Câu 5: syms n >> symsum(sym((-1)^n/n^2),1,inf) ans = -pi^2/12