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Chapter 36

Chapter 36. Partial fractions & their application. Let see the example below :. If the 2 fractions are added together, the result :. is more complicated than the previous two fractions.

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Chapter 36

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  1. Chapter 36 Partial fractions & their application By Chtan FYHS-Kulai

  2. Let see the example below : If the 2 fractions are added together, the result : By Chtan FYHS-Kulai

  3. is more complicated than the previous two fractions. If you want to integrate or expand the fraction, it is much simpler to express it as the sum of the two fractions. We call these fractions – the partial fractions. By Chtan FYHS-Kulai

  4. Expression of a fractional function in partial fractions : (Rule 1) : Before a fractional function can be expressed directly in partial fractions the numerator must be of at least one degree less than the denominator. By Chtan FYHS-Kulai

  5. e.g. 1 can be expressed in partial fractions. cannot be expressed directly in partial fractions. By Chtan FYHS-Kulai

  6. can be simplified before it can be expressed as a sum of partial fractions. By Chtan FYHS-Kulai

  7. (Rule 2) : Corresponding to any linear factor ax+b in the denominator of a rational fraction there is a partial fraction of the form , A is a constant. By Chtan FYHS-Kulai

  8. e.g. 2 Express the function in partial fractions. Soln : By Chtan FYHS-Kulai

  9. Let x=-2, -4=C(-3)(-3) Let x=1, 2=A(3)(3) Let x=-1/2, -1=B(-3/2)(3/2) By Chtan FYHS-Kulai

  10. (Rule 3) : Corresponding to any linear factor ax+b repeated r times in the denominator, there will be r partial fractions of the form By Chtan FYHS-Kulai

  11. e.g. 3 Express as a sum of partial fractions, Soln : By Chtan FYHS-Kulai

  12. If x=-1, -1=-8D, D = 1/8 If x=1, -1=2C, C = -1/2 If x=0, -3=A-B+C-D -3=A-B-5/8, A-B=-19/8 1 If x=2, 5=3A+3B+3C+D 5=3A+3B-11/8, A+B=17/8 2 By Chtan FYHS-Kulai

  13. 1+2 : 2A=-2/8, A=-1/8 B=9/4 By Chtan FYHS-Kulai

  14. (Rule 4) : Corresponding to any quadratic factor in the denominator there will be a partial fraction of the form By Chtan FYHS-Kulai

  15. e.g. 4 Express as a sum of partial fractions, Soln : By Chtan FYHS-Kulai

  16. Put x=1, -1=4D, D=-1/4 Put x=-1, -3=-4C, C=3/4 Put x=0, -2=-B-C+D, -2=-B-3/4-1/4, B=1 Put x=2, 6=(2A+1)(3)+5C+15D 6=3(2A+1), A=1/2 By Chtan FYHS-Kulai

  17. By Chtan FYHS-Kulai

  18. Note : Repeated quadratic factors in the denominator are dealt with in a similar way to repeated linear factors. By Chtan FYHS-Kulai

  19. Ex 16a p. 216 Mathematics 3 Q 3, 4, 5, 6, 9, 11, 12, 13, 15, 17, 20, 23, 27, 30, 32 By Chtan FYHS-Kulai

  20. The expansion of rational algebraic fractions By Chtan FYHS-Kulai

  21. Refer to textbook p.217 example 5 and example 6. By Chtan FYHS-Kulai

  22. Ex 16b p. 218 Mathematics 3 Q 3, 5, 9, 11, 13, 17, 20 By Chtan FYHS-Kulai

  23. The integration of rational algebraic fractions By Chtan FYHS-Kulai

  24. The following types of partial fractions will arise : Beyond the scope of this book . We can integrate these types of partial fractions. By Chtan FYHS-Kulai

  25. e.g. 5 Integrate with respect to x. Soln : By Chtan FYHS-Kulai

  26. When x=1, 1=2C, C=1/2 When x=-1, 1=2B, B=1/2 When x=0, 1=-A, A=-1 By Chtan FYHS-Kulai

  27. By Chtan FYHS-Kulai

  28. Ex 16c p. 220 Mathematics 3 All odd numbers. By Chtan FYHS-Kulai

  29. Misc. Ex. p. 221 Mathematics 3 All odd numbers. By Chtan FYHS-Kulai

  30. The end By Chtan FYHS-Kulai

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