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Conceptual Idea of a Limit Example: Left-hand limit: We say that the limit of f (x) as x tends towards c from the left is L if f (x) is very close to L whenever x is very close to, but less than, c. 1 lim x 0 x This is denoted by: lim f ( x) L xc Right-hand limit: We say that the limit of f (x) as x tends towards c from the right is L if f (x) is very close to L whenever x is very close to, but greater than, c. 1 lim x0 x This is denoted by: lim f ( x) L x c The limit: We say that the limit of f (x) as x tends towards c is L if f (x ) if the left-hand and right-hand limits exist and are both equal to L. This is denoted by: lim f ( x) L 1 x0 x lim Does Not Exist x c Note: Later, we will make this idea more formal by more rigorously specifying what we mean by “tends toward” and “very close”. We will want to specify that f (x) is arbitrarily close to L whenever x is close ‘enough’ to c.