Congratulations everybody. We have two units left to go. The first topic is partial fraction decomposition. Since it is not a large unit, it will not have its own assessment. We will finish it this week. Next week we will start our last unit, which is limits. The assessment for limits will include material on partial fractions. If you combine two fractions through addition or subtraction, you find the common denominator then add or subtract the adjusted numerators to get your answer. For example, x /3 + (x-1) / 4 = (4x / 12) + 3(x-1) / 12 = (4x + 3x-3) /12 = (7x-3) / 12. You can think of partial fractions as doing the opposite. Instead of being asked to add fractions together, you are being given the final sum of (7x-3) / 12 and asked to find the fractions that were added to get that value, in this case x/3 and (x-1)/4. There is a process to do this. It often involves solving a system of equations with multiple variables. This is where knowing how to find determinants on your calculator and using Cramer's Rule becomes useful, especially when solving systems with many variables. Homework - Due Friday - 5/29/20 page 720 - #'s 2, 12, 14, 16, 18, 22, 24, 26, 28, 32, 36 Videos: Setting up the partial fraction decomposition - (determines how many linear and quadratic factors you will need to find). www.youtube.com/watch?v=N1lx9yn3SLI&feature=youtu.be Example one with 2 linear factors www.youtube.com/watch?v=WoVdOcuSI0I&feature=youtu.be Example two with 2 linear factors www.youtube.com/watch?v=RFTAVAWHgN0&feature=youtu.be Example with repeated linear factors www.youtube.com/watch?v=6DdwGw_5dvk&feature=youtu.be Example with linear and quadratic factors www.youtube.com/watch?v=prtx4o1wbaQ&feature=youtu.be Example with repeated quadratic factors www.youtube.com/watch?v=Dupeou-FDnI&feature=youtu.be Another example www.youtube.com/watch?v=04RSkBwVzK0&feature=youtu.be
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