University:
Whitman College
Course:
MATH-125 | Calculus I
Academic year:

2022
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227

Pages:

1
Author:

ilikemyicons0y5

MATHS TYPES OF DISCONTINUITIES Removable type of discontinuities In case limf(x)exists but is not equal to f(a) then the function is said to have a removable discontinuity or discontinuity of the first kind. In this case we can redefine the function such that lim x -> a f(x) = f(a) * delta make it continuous at x = a Removable type of discontinuity can be further classified as: x overline z Missing point discontinuity Where lim x -> a f(x) exists but f(a) is not defined. Isolated point discontinuity Where lim x -> a f(x) exists & f(a) also exists but; lim x a f(x) ne f(a). Non-Removable type of discontinuities In case lim x -> a f(x) does not exist then it is not possible to make the function continuous by redefining it. Such a discontinuity is known as non-removable discontinuity or discontinuity of the 2nd kind. Non-removable type of discontinuity can be further classified as: Finite type discontinuity In such type of discontinuity left hand limit and right hand limit at a point exists but are not equal. Infinite type discontinuity In such type of discontinuity atleast one of the limit viz. LHL and RHL is tending to infinity. Oscillatory type discontinuity eg. f(x) = sin(pi/x) x = 0 f(x) = sin(pi/x) y = sin(s / x) f(x) has non removable oscillatory type discontinuity at x = 0 Example From the adjacent graph note that fis continuous at x = - 1 L fhas isolated discontinuity at x = 1 fhas missing point discontinuity at x = 2 iv. f has non removable (finite type) discontinuity at the origin.

Types of Discontinuities

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