derivative of x^x^x^x^x^x^x^x... as the power increases to infinitive

Answer 1

y = x^x^x^...
lny = x^x^x^... lnx = y lnx
lny/y = lnx
Now differentiating implicitly,

1/y y' - lny/y^2 y' = 1/x
y' = (1/xy)/(1 - lny/y)
You can massage that in various ways.

Answer 2

The first five square numbers are 1, 4, 9, 16, and 25, and their average is 11. What is the average of the next five square numbers?

Answer 3

well, just add 'em up and divide by 5. The numbers are

36,49,64,81,100

Answer 4

A jug contains 1
2 L of water.
The water is shared equally among 5 children.
How much water does each child receive?
A 1
10 L
B 1
5 L
C 2
5 L
D 5
2 L

Answer 5

2L/5child = 2/5 L/child