From sec 2.1 : Find: OUR GOAL Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS.

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Presentation transcript:

From sec 2.1 : Find: OUR GOAL Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Example: Find We say that the limit of f(x) as x approaches 2 from the right is equal to 4 The symbol x  2+ means that we consider only values of x > 2 We say that the limit of f(x) as x approaches 2 from the left is equal to 4 The symbol x  2- means that we consider only values of x < 2 Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

For the function whose graph is given below Determine the following limits Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Exam-I Term-122 Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Find: 1 Create a table: watch the behavior 2 Use the Graph to find the limit Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Example: Find Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Example: Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

- Can we use Direct Substitution Prop.?? Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Can we use Direct Substitution Prop.?? Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Find: 1 Create a table: watch the behavior 2 Use the Graph to find the limit 3 Given the function f(x) Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Exam-1 Term 122 1)Common Factors 2)Conjugate radical case Exam-1 Term 121 Example Example: Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

1)Common Factors 2)Conjugate radical case Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

What is the difference ?? Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Squeeze theorem = Sandwich theorem Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Example: Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Exam1-091 Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Limit from one side does not exist Find an example for a function such that the limit from right does not exist Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

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