Continuity on Open & Closed Intervals Objective: Be able to describe where a function is continuous and classify any discontinuities as removable or non-removable. - ppt download

Removable Vs. Non-Removable Discontinuities If a function f is defined on an interval and f is not continuous at c, then f is said to have a discontinuity at c. A discontinuity is removable if f can be made continuous by appropriately defining (or redefining) f(c). Otherwise the discontinuity is non-removable. Examples:
1.f(c) is defined. 2. exists. 3. Continuity on an open interval: A function is continuous on an open interval (a, b) if it is continuous at each point in the interval. A function that is continuous on the entire real line (-∞,∞) is everywhere continuous..
Non-Removable Discontinuities If a function f is defined on an interval and f is not continuous at c, then f is said to have a discontinuity at c. A discontinuity is removable if f can be made continuous by appropriately defining (or redefining) f(c). Otherwise the discontinuity is non-removable. Examples:.
Examples Discuss the continuity of each function.
Definition of Continuity on a Closed Interval A function f is continuous on the closed interval [a, b] if it is continuous on the open interval (a, b) and The function f is continuous from the right at a and continuous from the left at b.
Find a such that the function is continuous on the entire real line..

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Continuity and Discontinuity of Functions