EXAMPLES OF DIFFERENTIAL COEFFICIENTS. 173 



13. If x* + 2ax*y - ay 3 = 0, shew that -/ = 0, or + V2, 



when x = and y = 0. 



14. If x* - ay* + 2axy* + 3ax*y = 0, shew that -/- = 0, or - 1 , 



UtX/ 



or 3, when ie = and ?/ = 0. 



15. If a^c 3 + x*y ay* = 0, shew that - = 1, when x = 



and y 0. 



16. If ay = (a 2 - /) (6 + 2/) 2 , shew that g = ^^> 



when a; = and = b. 



17. If (^-^)(a:- 



find -if- when a; and y vanish, and when x 1, y = 1. 



//19\ , -1 + ^(33) 

 J {) and - --^ -' . 



18. If y* - 1/ 8 + Secy - 2x* = 0, find when x = 0. 



2 



Result 1, 2, or -. 

 Jj 



19. Find if if 





****. 



OA Tr 3 i * c. J J 



20. If - + ^ + --1 = 0, find -5-5 ^ T-, and -T-J. 

 a 6 c ax 8 



