114 PRACTICAL MATHEMATICS 



(22) Using Taylor's Expansion, find the approximate root of 

 the equation x 5 - 8x 3 + I2x - 185 = 0, knowing that the root lies 

 between 3 and 4. 



(23) If ~ - 2 -J- + 5y = 0, express y as a series of ascending 



dx doc 



dii 

 powers of x, knowing that when as = 0, y = and -^- = 2. 



(24) If (1 + x) -r^ +2-^ = 0, express y as a series of ascend- 



' ax 2 ax 



dij 

 ing powers of x, knowing that when x = 0, y = and -j- = 1. 



(25) If x ~ + ~ + y = 0, express y as a series of ascending 



dx dx 



powers of x, knowing that when x = 0, y = 1. 



