Limits
One Sided limits
One sided limit has two different kind, lift-hand limit (limit from left side) and right-hand limit (limit from right side).
1 Left Hand limit : x approaches a form the left or from values less than a.
2 Right Hand limit : x approaches a from the right or from values greater than a.
Example of One Side limits
find the one_sided limits of f(x) = [x^2-1, x≥0], [-x+1, x<1=0] as approaches 0.
The graph above, we can determine lim_(x->0^-1) f(x)=1 and lim_(x->0^+) f(x)=-1
This also can be determined algebraically lim_(x->0^->1) (-x+1) = 0+1 = 1 and lim_(x->0^+) (x^2-1) = 0^2 -1 = -1
Lim_(x -> 0) f(x) exist if and only if lim_(x->0^-) f(x) = lim_(x->0^+) f(x)
--> We will know more about existence of limit in subsequent section.