Verified answer

Proof by contradiction.

Claim that the limit does exist

(therefore, it must be some fixed number, with a finite value).

Call it Q (or whatever else you want).

If the limit exists, then the sequence

x = 1/2 1/4, 1/8, 1/16, ... 1/2^n ... should converge to Q (it should get closer and closer to Q).

If the limit exists, then the sequence

x = -1/2, -1/4, -1/8, -1/16, ... -1/2^n ... should converge to the same Q

Let delta be the distance between two values +1/2^n and -1/2^n

This distance is 1/2^(n-1) as n increases,

the distance gets smaller and smaller as n increases (delta gets smaller and smaller).

Therefore, the distance between f(1/2^n) and f(-1/2^n) should also get smaller and smaller (epsilon) as they both converve to Q

...

They don't.

contradiction.

The hypothesis (that Q does exist) must be false.