If For what value (s) of a does exists?

Given function is

There are three cases.

Case 1: When a = 0

:

⇒

⇒

Here

∴ does not exist.

Case 2: When a < 0

:

⇒

⇒

∴

∴ lim(f(x)) exists at x = a when a < 0

Case 3: When a > 0

:

⇒

⇒

∴

∴ lim(f(x)) exists at x = a when a > 0

Ans. exists for all a ≠ 0