Question

definition for continuity?

Answer 1

\[f(x) = \frac{1}{x - 1 } \]
the function is discontinuous at x=1

Answer 2

i just need a written definition for what it is

Answer 3

A function \(f:\mathbb{R}\to\mathbb{R}\) is continuous at some point \(a\) if \(\lim_{x\to a}f(x) = f(a)\)

Answer 4

Continuity means that the value of f(x) exists for all values of x

Answer 5

thank you snaef999

Answer 6

The function is continuous if it is continuous at all points.

Answer 7

snaef999 thats incorrect.

Answer 8

on a given interval..?

Answer 9

A function can be defined for all values yet fail to be continuous. See point discontinuity or step discontinuity.

Answer 10

Yes that is true.

Answer 11

A correct definition of continuity requires the concept of limit.