LIMITS OF A

FUNCTION

Reporter:

Miss Louie Joy J. Rosit

LIMITS OF A FUNCTION

A function f(x) is said to approach a value A as x

approaches a, if corresponding to every positive number

Є there is some positive number such that

is true for every x that satisfies the inequality

THEOREMS ON LIMIT:

THEOREMS ON LIMIT:

EXAMPLES:

EXAMPLES:

EXAMPLES:

CONTINUITY AND DISCONTINUITY

A single-valued function f(x) is said to be

continuous at a value a of its domain

provided that:

A function that is not continuous at a point is

said to be discontinuous at that point.

THEOREMS ON CONTINUITY

THEOREMS ON CONTINUITY

THEOREMS ON CONTINUITY

THEOREMS ON CONTINUITY

EXAMPLES:

x -4 -2 0 2 4

f(x) 16 4 0 4 16

EXAMPLES:

x -2 -1 0 1 2

f(x) -1/2 -1 undefined 1 1/2

EXAMPLES:

EXERCISES:1) Evaluate:

2) Find the value or values of x for which the function

is discontinuous:

“I can do all things through Christ who

strengthens me..”

-Philippians 4:13