SINGLE VARIABLE CALCULUS. PART I: DIFFERENTIATION. PART A: DEFINITION AND BASIC RULES. UNIT 0: LIMITS REVIEW. PART 3: Limit of quotients

  SINGLE VARIABLE CALCULUS

PART I: DIFFERENTIATION

PART A: DEFINITION AND BASIC RULES

UNIT 0: LIMITS REVIEW

PART 3: Limit of quotients

Limit of quotients

I. Limit Law for Division  

Limits and division

                    

          Limit Law for Division 

     

If $$\lim↙{x→a}f(x) = L$$ and $$\lim↙{x→a}g(x) = M$$ then:

•     If $M$≠$0$ , then $$\lim↙{x→a}{f(x)}/{g(x)} = L/M$$ 
•     If $M = 0$ but $L  ≠ 0$, then $$\lim↙{x→a}{f(x)}/{g(x)} = L/M$$ does not exist
•     If both $M = 0$ and $L = 0$ then $$\lim↙{x→a}{f(x)}/{g(x)} = L/M$$ might exist or not. More work is needed to determine whether the last type of limit exist, and what it is if it does exist.

Using the Division Law

Infinite Limits

Infinite Limits 2