Limits
2.0 Definition of Limit - In a different form:
2.1 One - Sided Limits:
2.2 Left hand Limit of a function:(LHL)
2.3 Right hand Limit of a function:(RHL)
2.0 Definition of Limit - In a different form:
2.2 Left hand Limit of a function:(LHL)
2.3 Right hand Limit of a function:(RHL)
Let $f(x)$ be a function defined for all $x$ in the $nbd(a)$ except possibly at $a$, then $L$ is said to be limit of $f(x)$ as $x$ tends to $a$, if the numerical difference between $f(x)$ and
$L$ can be made as small as we please by taking $x$ sufficiently close to $a$ but not equal to $a$.
we write this as $\mathop {\lim }\limits_{x \to a} f(x) = L$
NOTE:
- The limit of $f(x)$ at $a$ exists if $f(x)$ is well defined on neighbourhood of $x$=$a$ (but not necessarily at $a$) and has an unique behavior in the neighbourhood of $x$=$a$.
- ie; The limit of $f(x)$ at $a$ exists if $f(x)$ is well defined on deleted neighbourhood of $x$=$a$ and has an unique behavior in the neighbourhood of $x$=$a$.
