1. Calculus Notes 7.5 Inverse Trigonometric Functions & 7.7 Indeterminate Forms and L’Hospital’s Rule Start up: 1.(AP question) Compute (Text Question) In Example 2, why wasn’t the Quotient Rule used when taking the derivatives? We are not taking the derivative of. We are using l’Hospital’s Rule to evaluate

2. Calculus Notes 7.5 Inverse Trigonometric

3. Table of Derivatives of Inverse Trigonometric Functions

4. Calculus Notes 7.7 Indeterminate Forms and L’Hospital’s Rule Indeterminate form of type L’Hospital’s Rule: Suppose f and g are differentiable and near a (except possibly at a). Suppose that or that (In other words, we have an indeterminate form of type or.) Then if the limit on the right side exists (or is or ). Cauchy’s Mean Value Theorem: Suppose that the functions f and g are continuous on [a,b] and differentiable on (a,b), and for all x in (a,b). Then there is a number c in (a,b) such that

5. Calculus Notes 7.5 Inverse Trigonometric Functions Example 1: Find the exact value. Example 2: Simplify √3√3 2 30 ̊ 1 60 ̊ 90 ̊ √2 45 1 90 ̊ 1 1 θ x ?̊?̊ Example 3: Prove using implicit differentiation: Differentiate it implicitly with respect to x.

6. Calculus Notes 7.5 Inverse Trigonometric Functions Example 4: Find the derivative of Example 5: Find the limit

7. Calculus Notes 7.7 Indeterminate Forms and L’Hospital’s Rule Example 6: Find the limit. Us l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why. PS 7.5 pg.483 #1, 4, 12, 15, 18, 23, 25, 26, 32, 43, 47, 49, 53, 59 (14) PS 7.7 pg.501 #1, 5, 8, 15, 20, 38, 41, 63, 65, 78, 79, 85, [92] (12-[13]) Review Chapter 7 Worksheet #1-20