<Dl> <Dd> lim x → p − f (x) = L (\ displaystyle \ lim _ (x \ to p ^ (-)) f (x) = L) </Dd> </Dl> <Dd> lim x → p − f (x) = L (\ displaystyle \ lim _ (x \ to p ^ (-)) f (x) = L) </Dd> <P> respectively . If these limits exist at p and are equal there, then this can be referred to as the limit of f (x) at p . If the one - sided limits exist at p, but are unequal, there is no limit at p (the limit at p does not exist). If either one - sided limit does not exist at p, the limit at p does not exist . </P> <P> A formal definition is as follows . The limit of f (x) as x approaches p from above is L if, for every ε> 0, there exists a δ> 0 such that f (x) − L <ε whenever 0 <x − p <δ . The limit of f (x) as x approaches p from below is L if, for every ε> 0, there exists a δ> 0 such that f (x) − L <ε whenever 0 <p − x <δ . </P>

When do we say a limit does not exist