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

x f(x) ?

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

I. Direct Substitution Example 3: Find the limit

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

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

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)

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)

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

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