Difference between continuos and Dis continous function with example in proper line
Answers
Continuity
To understand continuity, it helps to see how a function can fail to be continuous. All
of the important functions used in calculus and analysis are continuous except at isolated
points. Such points are called points of discontinuity. There are several types. Let’s begin
by first recalling the definition of continuity (cf. book, p. 75).
(2) f(x) is continuous at a if limx→a
f(x) = f(a).
We say a function is continuous if its domain is an interval, and it is continuous at every
point of that interval.
A point of discontinuity is always understood to be isolated, i.e., it is the only bad point
for the function on some interval.
We illustrate the point of these definitions. (They are slightly different from the ones in
your book, but are more consistent with standard terminology in calculus.)
Answer:
A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value. Point/removable discontinuity is when the two-sided limit exists, but isn't equal to the function's value
Explanation:
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