Limit

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Suppose f x R R is defined on the real line and a L R It is said to be the limit of f as x approaches a is L and written as limit What is Limit of a function limx a f x L Definition Let f be a function defined on some open interval that contains the number a except possibly at a itself Then we say that the limit of f x as x approaches a is L and we write limx a f x L if for every number 0 there is number 0 such that if 0 x a then f x L Rules of Limit If L M c and k are real numbers and limx c f x L and limx c g x M then 1 Sum Rule limx c f x g x L M 2 Difference Rule limx c f x g x L M limx c k f x k L Rules of Limit 4 Product Rule limx c f x g x L M 6 Power Rule 3 Constant Multiplication Rule f x n Ln n a positive integer limx c 7 Root Rule limx c pn f x n L L 1 n n a positive integer One sided Limits While defining the limit of a function f as x approaches a we have considered the values of f in the deleted neighbourhood of a If we consider the behaviour of f for those values of x greater than a we say that x approaches a from the right or from above We denote this as x a Similarly if we consider the value of f for x less than a then we say that x approaches a from the left or from below We denote this as x a

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