One Sided Limit

==2024-11-17

Theory

${\lim }_{x\to c}f(x)$ if exists, means $f(x)$ can be approached from both sides left and right at an interior point c.

${\lim }_{x\to c^{-}}f(x)$ is the limit of the function when c is approached from left.

Similarly, ${\lim }_{x\to c^{+}}f(x)$ is the limit of the function when c is approached from right.

That means, $\lceil c^{+}\rceil =c+1$ and $\lfloor c^{+}\rfloor =c-1$

${\lim }_{x\to c^{+}}f(x)$ is right hand limit ${\lim }_{x\to c^{-}}f(x)$ is left hand limit

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PTR