Transcript:

Ok, so yesterday, we considered how 1/x, the function, can be used to solve a supposedly complicated problem. But here's another one: Which one of these is greater, (pi^e) or (e^pi)? Which one is greater? Again, use the function 1/x. 

This is the plot of 1/x, and here is e, and here is pi, and obviously, e is less than pi. So, the orange rectangle formed by e and pi as the limits is going to have an area which is going to be greater than the area of the blue curve, which is 1/x. 

So here's the area of the rectangle: which is width times height. Height is 1/e, and width is (pi-e). And the area under this blue curve is this integral, and you can solve it. 

And this and then you can do this, and then you can do this, and there you go. (e^pi) is greater than (pi^e). Again, we can easily solve this using the function 1/x. It's brilliant.