Question

if left hand and right hand side is zero for limit is it exist?​

Answer 1

Answer:

Suppose f : R → R is defined on the real line and p,L ∈ R. It is said the limit of f, as x approaches p, is L and written as

\lim_{x \to p}f(x) = L, \

if the following property holds:

For every real ε > 0, there exists a real δ > 0 such that for all real x, 0 < | x − p | < δ implies | f(x) − L | < ε. The value of the limit does not depend on the value of f(p), nor even that p be in the domain of f.

The reason why limit of function not exist when its right hand limit and left hand limit are different because you cannot find a ε to satisfy the above condition