5.1. Types of Discontinuity: Let f be a function defined as f:X-R and let xe X...

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5.1. Types of Discontinuity: Let f be a function defined as f:X-R and let xe X and let left hand limit, right hand limit, limit of the function and the value of the function at xare denoted by lim f(x). lim f(x), lim f(x) and f(x) respectively. Then (I) Removable Discontinuity at x, The function f:XR is said to have the removable discontinuity at x, EX, if the limit of the function exist at x, but not equal to the value of the function at x, i.e., lim f(x)= f(x). of fa (II) Discontinuity of the First Kind at x The function f:XR is said to have a discontinuity of first kind at x, if both the left hand limit and right hand limit exist at x, but are not equal to each other i.e. lim f(x)lim f(x) 5.1. Types of Discontinuity: Let f be a function defined as f:X-R and let xe X and let left hand limit, right hand limit, limit of the function and the value of the function at xare denoted by lim f(x). lim f(x), lim f(x) and f(x) respectively. Then (I) Removable Discontinuity at x, The function f:XR is said to have the removable discontinuity at x, EX, if the limit of the function exist at x, but not equal to the value of the function at x, i.e., lim f(x)= f(x). of fa (II) Discontinuity of the First Kind at x The function f:XR is said to have a discontinuity of first kind at x, if both the left hand limit and right hand limit exist at x, but are not equal to each other i.e. lim f(x)lim f(x)