1. Could be solved with complete the square and trig substitution. The Method of Partial Fractions can also be used, typically is easier. Could be solved with complete the square and trig substitution. The Method of Partial Fractions can also be used, typically is easier.

2. Lesson 7.5 Partial Fractions The purpose of today's lesson is to decompose a fraction into simpler rational expressions to which we can apply the basic integration formulas. This technique was introduced in 1702 by John Bernoulli (Swiss mathematician). Quote of the Day: "Five out of four people have trouble with fractions." -- Steven Wright

3. 1.Divide if improper 2.Factor denominator into product of linear and irreducible quadratic factors. 3.Decompose into partial fractions Partial Fractions to integrate Rational Functions. Each repeating factor is a separate fraction

4. To find the coefficients in the numerator: 1.Clear out denominators. 3 Ways to solve for A, B, C, … 2. 3 Ways to solve for A, B, C, … i.Group like terms and Equate Coefficients Method ii.Plug in different x-values and solve the system iii.Heaviside method: Can be used if all the factors in denom. are linear/non-repeating. Plug in each root To find the coefficients in the numerator: 1.Clear out denominators. 3 Ways to solve for A, B, C, … 2. 3 Ways to solve for A, B, C, … i.Group like terms and Equate Coefficients Method ii.Plug in different x-values and solve the system iii.Heaviside method: Can be used if all the factors in denom. are linear/non-repeating. Plug in each root

5. 1.Linear – non-repeating factors

6. Use the 2 nd method to solve for the numerators 1.Linear – non-repeating factors

7. Heaviside method Use the Heaviside method to solve for numerators. Put finger over the zero in denominator and plug in the zero to the rest of the left side. Heaviside method Use the Heaviside method to solve for numerators. Put finger over the zero in denominator and plug in the zero to the rest of the left side. 1.Linear – non-repeating factors

8. 1.Linear – Repeating factors Each repeating factor is a separate fraction

9. 1.Linear – Repeating factors

10. Homework Homework HW 29 p. 522 #7-9, 11, 12, 14-19 Review handout

11. Agenda Feb. 20 Homework questions Finish Partial Fractions Decomposition Due tomorrow: Droodle Review Book Problems: p. 522 # 21-23, 29, 41, 58 Tomorrow and Friday: Revisiting Limits Exam corrections

16. 2. Non-Linear factor