The document discusses limits of functions and continuity. It defines a limit of a function as approaching a value A as the input x approaches a number a. A function is continuous at a point a if the limit exists and equals the function value at a. A function is discontinuous if it is not continuous at a point. Examples of continuous and discontinuous functions are provided to illustrate the concepts.

1. LIMITS OF A
FUNCTION
Reporter:
Miss Louie Joy J. Rosit

2. 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

3. THEOREMS ON LIMIT:

4. THEOREMS ON LIMIT:

5. EXAMPLES:

6. EXAMPLES:

7. EXAMPLES:

8. 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.

9. THEOREMS ON CONTINUITY

10. THEOREMS ON CONTINUITY

11. THEOREMS ON CONTINUITY

12. THEOREMS ON CONTINUITY

13. EXAMPLES:
x -4 -2 0 2 4
f(x) 16 4 0 4 16

15. EXAMPLES:
x -2 -1 0 1 2
f(x) -1/2 -1 undefined 1 1/2

17. EXAMPLES:

19. EXERCISES:
1) Evaluate:
2) Find the value or values of x for which the function
is discontinuous:

20. “I can do all things
through Christ who
strengthens me..”
-Philippians 4:13