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5017 Partial Fractions

5017 Partial Fractions. AP Calculus. Partial Fractions. Remember: Adding Fractions Butterfly Method: Decomposition: GIVEN : SUM FIND: ADDENDS ( Like Factoring- given the product ( answer ) want to find the problem). Steps:. ** Check if proper fraction

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5017 Partial Fractions

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  1. 5017 Partial Fractions AP Calculus

  2. Partial Fractions Remember: Adding Fractions Butterfly Method: Decomposition:GIVEN: SUM FIND: ADDENDS ( Like Factoring- given the product (answer) want to find the problem)

  3. Steps: • ** Check if proper fraction • Factor the denominator and write the addition problem. • Write fraction addition problem using a numerator one degree • less than the denominator; may have repeated factor. If • Linear factors, use • b. Quadratic factors, use • 3. Add the new fraction; find LCD, etc. • 4. Set numerators equal. • 5. Solve a. Convenient x-values. b. Equate the coefficients.

  4. Examples: Linear factors Example 1: Linear factors

  5. Examples: Linear factors Example 2: Linear factors

  6. Logistic Growth

  7. Examples: Repeated Linear factors Example 3: Repeated Linear Factors Must do all possibilities up to the given exponent.

  8. Examples: Repeated Linear factors Example 4: Repeated Linear Factors

  9. Examples: Quadratic Factors Example 5:

  10. Examples: Quadratic Factors Example 6:

  11. Examples: Quadratic Factors Example 7:

  12. Last Update: • 03/08/10

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