# 指数函数的图形比较

```% Define the mesh x = 0:0.16:5; y = 0:0.16:5; [xx,yy] = meshgrid(x,y); % The plot zz = xx.^yy-yy.^xx; h = surf(x,y,zz); h.EdgeColor = [0.7 0.7 0.7]; view(20,50); colormap(hsv); title('\$z = x^y-y^x\$','Interpreter','latex') xlabel('x') ylabel('y') hold on```

${\mathit{x}}^{\mathit{y}}-{\mathit{y}}^{\mathit{x}}=0$ 方程解的形状较为特别，单纯通过观察并不足以解决我们一开始的问题。下图是使得 $\mathit{z}=0$xy 值。

```c = contourc(x,y,zz,[0 0]); list1Len = c(2,1); xContour = [c(1,2:1+list1Len) NaN c(1,3+list1Len:size(c,2))]; yContour = [c(2,2:1+list1Len) NaN c(2,3+list1Len:size(c,2))]; % Note that the NAN above prevents the end of the first contour line from being % connected to the beginning of the second line line(xContour,yContour,'Color','k');```

`plot([0:5 2 4],[0:5 4 2],'r.','MarkerSize',25);`

```e = exp(1); plot([e pi],[pi e],'r.','MarkerSize',25); plot([e pi],[pi e],'y.','MarkerSize',10); text(e,3.3,'(e,pi)','Color','k', ... 'HorizontalAlignment','left','VerticalAlignment','bottom'); text(3.3,e,'(pi,e)','Color','k','HorizontalAlignment','left',... 'VerticalAlignment','bottom'); hold off;```

```e = exp(1); e^pi```
```ans = 23.1407 ```
`pi^e`
```ans = 22.4592 ```