# Another problem

1. May 7, 2005

### abia ubong

how do i find the area of a rectanglewith sides 400root of 400 raised continously to itself like x^x^x^..and 800root of 800 raised also to itself continouslylike y^y^y...
leave answer in whole number not exponent

2. May 7, 2005

### dextercioby

What do those "..." mean...?I can assume you'd have to evaluate

$$400^{400^{400^{...}}}\cdot 800^{800^{800^{...}}}$$

Daniel.

3. May 7, 2005

### HallsofIvy

Do you have any reason to think that such a sequence converges?

4. May 7, 2005

### dextercioby

Read mathworld's page on the power tower.I'm sure u'll find the upper limit for the convergence interval,that is,of course,if u meant the infinite superpower of 400 and 800 respectively.

Daniel.

5. May 7, 2005

### saltydog

Abia, consistent no doubt. I think you mean a power tower like:

"The 400'th root of 400"

$$\sqrt[400]{400}\approx 1.01509$$

I think that's in the range of convergence.

Edit: The 800 one too for that matter.

Last edited: May 7, 2005
6. May 8, 2005

### abia ubong

area of rectangle with lenght x^x^x^x^x.....
and breath y^y^y^y^y^y..... where x is 400^ 1/400 and y is 800^ 1/800.
leaving answer in whole number not decimal or exponent

7. May 8, 2005

### saltydog

Hello Abia. Yea, leaving it in whole numbers . . . hum . . . how about expressing the power towers in terms of Lambert W-functions (which can be done and in whole numbers), and in this way then the area is just a product of two such expressions.

8. May 8, 2005

### mathelord

do not understand
pls explain

9. May 8, 2005

### saltydog

Check out Power Towers, and Lambert W-functions in MathWorld. Try that first.