Limit is the value that a function approaches as the input approaches some value.
limit notation : $$\lim_{x\to{c}}f(x)=L$$
For example:
$$f(x)=x^2$$ and x value approaches 2 then
when x=1.8 then $f(1.8)=3.24$
when x=1.9 then $f(1.9)=3.61$
when x=1.99 then $f(1.99)=3.9601$
when x=1.999 then $f(1.999)=3.996001$
when x value approaches 2 , f(x) value approaches 4
$$\lim_{x\to{2}}x^{2}=4$$
We have two ways approaches some x value
1 from bigger number approaches to x value :
$$\lim\limits_{ x\to a^+ }f(x)$$ is right hand limit
2 from smaller number approaches to x value :
$$\lim\limits_{x\to a^-}f(x)$$ is left hand limit
and this two limit value must be same, and then we can have limit value at x = a
$$\lim\limits_{ x\to a^+ }f(x) = \lim\limits_{x\to a^-}f(x) = \lim\limits_{x\to \infty}f(x)$$
before we find out $\lim\limits_{ x\to 2 }x^2=4$ is left hand limit
( x value approaches from 1.8 , 1.9 , 1.99 , 1.999 , ···· )
how about right hand limit
$$f(x)=x^2$$ and x value approaches 2 then
when x=2.2 then $f(2.2)=4.84$
when x=2.1 then $f(2.1)=4.41$
when x=2.09 then $f(2.09)=4.3681$
when x=2.009 then $f(2.009)=4.036081$
when x value approaches 2 , f(x) value approaches 4
$$\lim_{x\to{2}}x^{2}=4$$
$$\lim_{x\to{2}^-}x^2 = \lim_{x\to{2}^+}x^2 = 4$$
$$\lim_{x\to{2}}x^{2}=4$$
remember $$\lim\limits_{ x\to a^+ }f(x) = \lim\limits_{x\to a^-}f(x) = \lim\limits_{x\to a}f(x)$$