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How to find the value of any number lets say 2 such that 2^2^2^2^2^....infinity! And also solve: min value of 2^(sinx-1) + 2^(cosx-1) is...??? root(2)^[root(2)] root(2)^ [-root(2)]


How to find the value of any number lets say 2 such that


 


2^2^2^2^2^....infinity!


And also solve:


min value of 2^(sinx-1) + 2^(cosx-1) is...???



  1. root(2)^[root(2)]

  2. root(2)^ [-root(2)]



Grade:12

1 Answers

Aman Bansal
592 Points
12 years ago

Dear Abhijat,

Value of such numbers in infinnite and can't be determined,

However we can find th limits of x^x^x^x........ by assuming y=x^x^x^ (1 term less then infinite terms )

Therefore y= x^y

Thus by taking LOG we can evaluate the limting value.

The minimum value of  2^(sinx-1) + 2^(cosx-1) is

root(2)^ [-root(2)]

Best Of luck

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