What is the definition of continuity at a point?

Question

t5an1izqp · Accepted Answer

A function             f              (        x        )             is said to be continuous at a if             lim              x        →        a                    f              (        x        )              =          f              (        a        )

Brianna Schmidt · Accepted Answer

Let             f              (        x        )             be a real function of real variable defined in the domain       I    ⊂    ℝ  .Let             x      0        ∈    I   be a point of accumulation for I.The function             f              (        x        )             is continuous in             x      0       if:            lim              x        →                  x          0                            f              (        x        )              =          f              (                  x          0                )            that is if the limit of             f              (        x        )             as x approaches             x      0       equals the value of the function in             x      0      . This means that as x gets closer and closer to             x      0      , then             f              (        x        )             gets closer and closer to             f              (                  x          0                )            , so that the graph of the function has no &quot;jumps&quot;.

What is the definition of continuity at a point?

Answered question

Answer & Explanation

New Questions in Differential Calculus