1. Objectives: 1.Be able to find the limit of a function using direct substitution. 2.Be able to find the limit of function that is in the indeterminate form. Critical Vocabulary: Limit, Direct substitution, Indeterminate Form Warm Up: Find the limit numerically and graphically

2. x f(x) -5 -9 -4 -7 -3.1 -5.2 -3.01 -5.02 -3.001 -5.002 -2 -3 -2.9 -4.8 -2.99 -4.98 -2.999 -4.998 -3 ?

3. I. Direct Substitution Example 1: Find the limit f(1) = (1) 2 + 1 f(1) = 1 + 1 f(1) = 2 Example 2: Find the limit

4. I. Direct Substitution Example 3: Find the limit

5. I. Direct Substitution Example 4: Find the limit Direct Substitution will not work on this because it yields an indeterminate form. Undefined

6. Section 3.3 Assignment Part 1 Page 226-228 #1-25 odd MUST SHOW YOUR WORK TO GET CREDIT!!!!

7. II. Indeterminate Form 1. Factor and Cancel 2. Rationalizing Technique (Use when you have a radical) 3. Use Algebra (Common Denominators/Expand) Then try to use direct substitution a second time!!!!!! Example 4: Find the limit f(-1) = 2(-1) - 3 f(-1) = -5 Causes a hole in the graph or an asymptote This graph will have a hole at (-1, -5)

8. II. Indeterminate Form 1. Factor and Cancel 2. Rationalizing Technique (Use when you have a radical) 3. Use Algebra (Common Denominators/Expand) Then try to use direct substitution a second time!!!!!! Example 5: Find the limit f(0) = 1/(0-1) f(0) = -1 Causes a hole in the graph or an asymptote This graph will have a hole at (0, -1)

9. II. Indeterminate Form 1. Factor and Cancel 2. Rationalizing Technique (Use when you have a radical) 3. Use Algebra (Common Denominators/Expand) Then try to use direct substitution a second time!!!!!! Example 6: Find the limit

10. Section 3.3 Assignment Part 2 Page 226-228 #31-49 odd, 57 MUST SHOW YOUR WORK TO GET CREDIT!!!!