I Q 1 3 1 Continuity from the Right at a Point A function f X R is said to be right continuous or continuous form the right at a

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I Q 1 3 1 Continuity from the Right at a Point A function f X R is said to be right continuous or continuous form the right at a point x EX if the right hand limit of f exists at x and equal to f x i e lim f x f x X 3 2 Continuity from the Left at a Point A function f X R is said to be Left continuous or continuous form the Left at a point x X if the Left hand limit of f exists at x and equal to f x i e lim f x f x X 4 Continuous Function A function f X R is said to be continuous on X if and only if f is continuous at each point of X Example 1 Show that the function f x is not continuous at x 0 Solution Given function is f x since f x is not defined for x 0 therefore it cannot be continuous at x 0 Moreover we know that lim f x lim does not exist in R Hence f x is not continuous at x 0 Value Addition Note If the limit of a function f X R does not exist at a point x X in R then the function f X R cannot be continuous at x

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