What is the infinity root of infinity

Unlimited spaces ??

Hey curlierfries,

You did everything right, your solution is right!

If you now determine the limit, you get the value "infinite" for the area (unlimited to the right), namely:

The area below is therefore getting bigger and bigger, although the graph tends towards 0.

Note: Not all improper integrals tend towards a (constant) value when the graph tends towards zero!

It depends on "how fast" the graph approaches zero, i.e. whether adding up the function values ​​(~ integral) actually increases the result.

To do this, a little thought experiment:

We both continue to build a tall tower, as follows:

On the first day I build half a meter, then a third of a meter, then a quarter of a meter, etc.

On the first day you build half a meter, then a quarter, then an eighth, etc.

The exciting thing now is:

We both build infinitely long
We're both building less and less every day
My tower will be infinitely large - not yours!

You are simply not building fast enough, plus your respective tower heights:



You can see that you actually only halve the distance every day .. So you never get beyond that!

Well, hopefully that was helpful ^^

The relationship:

(my tower growth)


(Your tower growth)