134 INDETERMINATE FORMS. 



(1 \sinor 

 - ) takes the form oo when x = ; also 



GT- 



XT -i smoj , 



Now, sma;loga; = .xlogx; 



27 



when x = 0, we have 



sina; 

 ~ =1 ' 



05logcc = 0, (Art. 158), 

 therefore sin x log x = 0, when a; = 0, 



(l\sin* 

 = 1, when x 0. 

 / 



\ ** 



/ ^ \tan 



Again, (2 -- ) '" takes the form 1, when x = a. 



-,, , . tan ^ log (2-?) 



The above expression = e 2a V a/ 



2 

 = e" when a; = a, (Art. 158). 



160. Form oo - oc . 



Let <f> (x) and ^ (a;) be two functions of x which become 

 infinite when x = a, then 



assumes the form oo oo ; it is required to find the value of 

 the expression. 



Put ? = *(*)-*(*), 



then e v -($>(*)-*(*) 



