WHEN INDETERMINATE IN FORM. 167 



It must be observed that this method is liable to an 



objection. We assume that , , -T-JJ and -> , -5^, vanish 



because in each case one factor vanishes ; if however -5? be 



ax 



infinite, it does not follow necessarily that r 2 an( j 



otady ofc* 



cPw d?y 



-y-; -7^ vanish. 



ay* <c 



192. Example. # 4 + 3c&y - 4aV?/ - aV = 0, or u = 0. 

 Here ( -^*J = - 4a*y - 2a 2 ic, 



, f dy 



' 6 5S = 4i/ 3 + 6a 2 y - 4aaj ~ 2/ + 3a 2 ?/ - 



Here x = 0, y = 0, satisfy M = 0, and make -p assume the 







form - . 



Differentiate both numerator and denominator, and we have 

 f- = the limit of 



therefore 



= ^ . 

 dx 3 



