140 INDETERMINATE FORMS 



The value of z is also determinate if 



\dx/ _ \dy) 



\dx) \dy) 



fdF 



then proceeding to a second differentiation we have 



: 



' 



which is generally indeterminate, since ty (x) is an arbitrary 

 function. 



Example 1. Suppose 

 logaj + 



fdf\ 1 



-,- = - = 1. when x = 1, 

 \dx) x 



_ log x + logy , ,_ 



~ ' B " 1 ' 5 - 



dy 



, , , 

 (a?) 



which is really indeterminate, and may assume any value 

 between + oo and oo . 



Example 2. Suppose 



= (a?-l 

 = 



Here z takes the form - when x 1 and y = 1. 



