PROPERTIES OF LIMITS BASIC CALCULUS.pptx

PROPERTIES OF LIMITS BASIC CALCULUS

1. PROPERTIES OF LIMITS BASIC CALCULUS Ms. Mia Elmore M. De Leon

2. PROPERTIES OF LIMITS OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification.

3. SUCCESS CRITERIA I can… Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. PROPERTIES OF LIMITS

4. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. Limits - describe  how a function behaves near a point , instead of at that point. This simple yet powerful idea is the basis of all of calculus. UNLOCKING

5. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Let f and g be two functions, and assume that and   Where L and M are real numbers (both limits exists).

6. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Property 1: The limit of a constant is itself.   for any constant   Example: 1.)     2.)     3.)    

7. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Property 2: The limit of as approaches is equal to .     (This may be thought of as substitution law, because is simply substituted by . )   Example: 1.)     2.)     3.)    

8. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Let f and g be two functions, and assume that and   Where L and M are real numbers (both limits exists).   Property 3: Limit of a Sum Example: 1.)        

9. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Let f and g be two functions, and assume that and   Where L and M are real numbers (both limits exists). Then   Example: 1.)         Property 4: Limit of a Difference 2.)        

10. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Property 5: The constant multiple property   for any constant   Example: 1.)               2.) If the then      

11. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Let f and g be two functions, and assume that and   Where L and M are real numbers (both limits exists). Then   Property 6: Limit of a Product Example: 1.) Let and        

12. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER   Property 6: Limit of a Product Example: 2.)              

13. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Property 7: Limit of a Quotient   If              

14. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Property 8: Limit of a Power   is real number   Example:          

15. PROPERTIES OF LIMITS SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. LESSON PROPER Property 9: Radical/Root Property   Example:        

16. SUCCESS CRITERIA I CAN. . . Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. OBJECTIVES Illustrate the properties of limits Apply limit properties Evaluate limit by direct substitution or by simplification. ACTIVITY       D etermine the limit algebraically, if it exists.