II I Discontinuity of the First Kind from the Left at x The function f X R is said to have a discontinuity of first kind from the left at x if the left hand limit exist at x but not equal to the value of the function at x i e lim f x f x II II Discontinuity of the First Kind from the Right at The function f X R is said to have a discontinuity of first kind from the right atx if the right hand limit exist at x but not equal to the value of the function atx i e lim f x f x X III Discontinuity of the Second Kind at x The function f X R is said to have a discontinuity of second kind at if both the left hand limit and right hand limit do not exist at x i e lim f x and lim f x do not exist III I Discontinuity of the Second Kind from the Left at x The function f X R is said to have a discontinuity of second kind from the left at x if the left hand limit does not exist at x i e lim f x does not exist X x III II Discontinuity of the First Kind from the Right at x The function f X R is said to have a discontinuity of second kind from the right at x if the right hand limit does not exist at i e lim f x does not exist x Value Addition Jump of a Function at x If a function f X R has a discontinuity of first kind at x then the function f is said to have a jump at x and the value of the jump is equal to the difference of both the limits at x i e Institute of Lifelong Learning University of Delhi Value of the jump at x lim f x lim f x 1 94 1 g Example 5 Show that the function f defined by sin x Continuity of Functions f x x DEL x 0 x 0 dementimuit pg 10 10