5-Limits dfdfdfdfdLaws.ppterrererererererefcfx

rgrthhhhhhhhhhhhhhfyjjjyh

1. LIMITS LAWS

2. illustrate the limit laws apply the limit laws in evaluating the limit of algebraic functions (polynomial, rational & radical). Learning Outcomes

3. What are laws and why are they created? Introduction

4. For sure there will be lots of explanation about it, one of which is that, it is a rule that is meant to be followed for greater good. Introduction

5. LIMIT LAWS The limit of a constant is itself. If k is any constant, then,   1. CONSTANT LAW

6. LIMIT LAWS The limit of 𝑥 as 𝑥 approaches 𝑐 is equal to c. That is,   2 . LIMIT OF ‘X’ LAW

7. LIMIT LAWS The limit of a constant 𝑘 times a function is equal to the product of that constant and its function’s limit.   3. CONSTANT MULTIPLE THEOREM

8. LIMIT LAWS The limit of a sum of functions is the sum of the limits of the individual functions.   4 . ADDITION THEOREM

9. LIMIT LAWS The limit of a difference of functions is the difference of the limits of the individual functions.   5. SUBTRACTION THEOREM

10. LIMIT LAWS The limit of a product of functions is the product of the limits of the individual functions.   6 . MULTIPLICATION THEOREM

11. LIMIT LAWS The limit of a quotient of functions is the quotient of the limits of the individual functions.   7. DIVISION THEOREM

12. LIMIT LAWS The limit of an integer power 𝑝 of a function is just that power of the limit of the function.   8. POWER THEOREM

13. LIMIT LAWS If 𝑛 is a positive integer, the limit of the 𝑛𝑡ℎ root of a function is just the 𝑛𝑡ℎ root of the limit of the function, provided that the 𝑛𝑡ℎ root of the limit is a real number.   9 . RADICAL/ROOT THEOREM

14. Examples 1. 2.  

15. Examples 3. 4.  

16. Examples 5 . 6.  

17. More Examples 1. 2. 3.  

18. Wrap-up Vic and Joey argue about the limit of the function 𝑓(𝑥) = as 𝑥 approaches 0. Vic’s opinion is that the limit is 0 while Joey claims that the limit does not exist. Write a short explanation that discusses the pros and cons of Vic and Joey’s opinion.  

19. THANK YOU!