Question

What is the condition for solving continuity in a closed interval?

Answer 1

A function f is continuous at a point a if the limit as x approaches a exists and is equal to f(a). That is, if
\[\lim_{x \rightarrow a-} f(x)= f(a) = \lim_{x \rightarrow a+} f(x)\]

Answer 2

K!

Answer 3

Continuity of a function becomes obvious from its graph.
If f(x) is continuous at all points in an interval (a, b), then f(x) is continuous on (a, b)
•f(x) is undefined at c
•The limx → c f(x) does not exist.
•Values of f(x) and the values of the limit differ at the point c
- If f(x) is continuous at all points in an interval (a, b), then f(x) is continuous on (a, b)
- A function continuous on the interval (-∞; +∞) is called a continuous function

Answer 4

A function f(x) is said to be continuous on a closed interval [a, b] if the following conditions are satisfied:
-f(x) is continuous on [a, b];
-f(x) is continuous from the right at a;
-f(x) is continuous from the left at b.

Answer 5

k!thanx i got it.