what is mean limit and continuity explain it perfectly

L IMIT OF A REAL F UNCTION :
f(x) be a function defined in a deleted nbd of ‘a’ and l ∈ R, for each ∈ > 0, there exists δ > 0
such that 0
we write it as Lt f(x) = l
x → a
R IGHT LIMIT OF ‘ F ’ AT ‘ A ’:
For each . ∈ > 0, there exist δ > 0 such that a
right limit of f(x) at ‘a’. Then we write it Lt f(x) = l.
x →a +
L EFT LIMIT OF ‘ F ’ AT ‘ A ’:
for each ∈ > 0, there exists a δ > 0 such that a – δ
limit of ‘f’ at ‘a’. Then we write it is Lt f(x) = l.
x →a −
Note: if Lt f(x) = Lt f(x) = l, then we say that limit of f(x) exists at x = a in this case limit
x →a −
x →a +
is denoted by Lt f(x): Lt f(x) = l.
x → a
x → a
I NFINITE LIMIT :
Let ‘f’ be a function defined in a deleted nbd of ‘a’. If for every k > 0 (how ever larger) ∃ δ >
0 such that 0 k then we write Lt f(x) = ∝.