Question

用matlab绘制z=x^y-y^x的图形来比较e^pi,pi^e大小（能附加图形么？

Answer 1

点展开看,
蛋疼的百度.
%两个思路
%其一,
z(x,y)写成
g(x)=z(x,pi)=x^pi-pi^x;
画图
x=linspace(2,3.5,100);
g=x.^pi-pi.^x;
plot(x,g);
hold
on
plot(x,zeros(size(x)),'k');
%
横轴
%
再画出x=e的直线.
plot(exp(ones(1,10)),
linspace(-4,2,10),'r');
text(exp(1),
exp(pi)-pi^(exp(1))+0.5,
'交点g(e)=z(e,\pi)');
%
注意交点处大于0
%
所以g(e)=z(e,pi)>0,
因此
e^pi
>
pi^e
%其二，绘制3d图
figure
g=linspace(2,3.5,100);
[x,y]=meshgrid(g,g);
z=x.^y-y.^x;
surf(x,y,z,'edgecolor','none','facealpha',0.5);
hold
on
z0=zeros(1,10);
plot3(z0+exp(1),
z0+pi,
linspace(-3,3,10),'k');
plot3(exp(1),
pi,
exp(pi)-pi^(exp(1)),
'ko','markerfacecolor','k')
xlabel('x');ylabel('y');zlabel('z')
mesh(x,y,zeros(size(x)),'edgecolor','none','facealpha',0.3,'facecolor','k');
view([130,18])
%
注意过(e,
pi)的直线与曲面交点在黑色平面之上,
说明z(e,pi)>0