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 ).