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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...
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...
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
Limits of functions
Limits of functions
Limits of functions
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Limits of functions

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Limits of a Function

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Limits of functions

  1. 1. LIMITS OF A FUNCTION Reporter: Miss Louie Joy J. Rosit
  2. 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. 3. THEOREMS ON LIMIT:
  4. 4. THEOREMS ON LIMIT:
  5. 5. EXAMPLES:
  6. 6. EXAMPLES:
  7. 7. EXAMPLES:
  8. 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. 9. THEOREMS ON CONTINUITY
  10. 10. THEOREMS ON CONTINUITY
  11. 11. THEOREMS ON CONTINUITY
  12. 12. THEOREMS ON CONTINUITY
  13. 13. EXAMPLES: x -4 -2 0 2 4 f(x) 16 4 0 4 16
  14. 14. EXAMPLES: x -2 -1 0 1 2 f(x) -1/2 -1 undefined 1 1/2
  15. 15. EXAMPLES:
  16. 16. EXERCISES: 1) Evaluate: 2) Find the value or values of x for which the function is discontinuous:
  17. 17. “I can do all things through Christ who strengthens me..” -Philippians 4:13

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