DISCONTINUOUS FUNCTIONS. 255 



, I — x\x I 1 — a;\ , 



^■= 1 + T^ 2+ I- n^^^'- 



X f \ — x\x X \ — X l\ — x\x 



2 +V 1 <n ^ J2 + 2 ~ TV^ '^\T^^j2 



\ fn X \ \ <r x' 



\ X X ar 



\v>x'^\inx~^\is\x \ <n X 



= \ -(\ -1x -\- 3? 



\ Vi X 



(1 - ^)-' 



1 - , 



\ <t> X 



Hence, 1 - \ — ^ is the function of x, which 



\ isi X 



expresses the relation of the two co-ordinates at 

 any point from A to B. The quantity 1 «> a- in 

 the above equation expressing the relation be- 

 tween the co-ordinates, apprize us at once that the 

 function of x^ and, consequently, the value of y^ 

 undergoes a complete change when x arrives at 

 unity. This value of Y may be used for all 

 purposes respecting the division of the triangle 

 ACB : thus, if it were required to find the area 



