Limits
Calculus is that branch of mathematics which mainly deals with the study of change in the value of a function as the points in the domain change.
Limit is used when we have to find value of a function near to some value. Eg: f( x) =( x 2-9)/( x-3). Find value of this function for x = near to 3.
Left hand limit: lim x→a – f( x)
Right hand limit: lim x→a + f( x). If right & left hand limits coincide, we call that common value as limit of f( x) at x = a & denote it by lim x→a f( x).
Algebra of Limits
Let f and g be two functions such that both lim x→a f( x) and lim x→a g( x) exist. Then
o Lim x→a [ f( x) + g( x)] = lim x→a f( x) + lim x→a g( x). o Lim x→a [ f( x) – g( x)] = lim x→a f( x) – lim x→a g( x).