Continuity

A function f, defined in an open interval centered at a, is said to be continuous in x = a if:

Or:

Otherwise, it is said that f is discontinuous.

Example:

f is continuous in R-{-2}

Properties: If f and g are continuous in a and k Є R

- k·f is continuous in a

- f±g is continuous in a

- f·g is continuous in a

- f/g is continuous in a, if g(a)≠0

- If f is continuous in a and g in f(a) →g_˚f is continuous in a

A function f is continuous in an open interval (a,b) if f is continuous

A function f is continuous in a closed interval [a,b] if f is continuous

Exercises:

1.- Is the function

continuous in x = 0?

2.- Let the function

a) Find the value of a to do f continuous in x = -2

b) For that value of a, is the function continuous in x = 2?

Solutions: 1.- Yes; 2.- a) a = 2/3; b) No