To prove the continuity of a function, is it possible to determine the continuity of a function in an interval as long as the continuity of two endpoints is proved (in an open and closed interval)?

To prove the continuity of a function, is it possible to determine the continuity of a function in an interval as long as the continuity of two endpoints is proved (in an open and closed interval)?

If limf (x) = f (x0) x - > x0, then f is continuous at x0
After introducing the concept of increment, the definition of continuity is equivalent to Lim △ y = 0 △ X - > 0
Or in the way of ε - δ: if for any ε > 0, there exists δ > 0, so that | x-x0 is appropriate|

The continuity and differentiability of the following functions at x = 0 are discussed
The continuity and differentiability of the following functions at x = 0 are discussed
1.y=∣sinx∣
2. Y = ① (x under the third radical) × (1 / x), X ≠ 0,
② 0,x=0

The continuity and differentiability of the following functions at x = 0 are discussed
1.y=∣sinx∣
The first is defined at x = 0, the second is Lim | SiNx | = 0 when x approaches 0, and the third is the limit value
So continuous
But it can't be induced

Try to discuss the continuity and differentiability of function f (x) = x | x ^ 2-x |

Let D1 = {x | x > 1 or X