Calculus, 8th Edition,stewart; page 82 problem 39

Question

If the function f is defined by

prove that does not exist.

Answer 1

Step:1

The function is .

Consider 

If for every number of , there exists a  such number  whenever .

Consider .

If  is rational the function value is .

If  is irrational the function value is .

The value of the function is not approaching to a unique value.

 does not exist.

Solution:

 does not exist.