TRACING OF CURVES. 



"371 



When x is very large the terms included in 'the &c. of 

 equation (5) will be very small compared with -- . Hence 



j i.t 



comparing (4) and (5) we see that corresponding to the same 

 abscissa the ordinate of the curve is less than that of the 

 asymptote, and therefore the curve lies below the asymptote 

 as represented in the figure. ., 



341. Example (2). Suppose 



/>* I O* , - sv\ { >y* __ 

 ,, i*/ \*y Lvy l/ 



x + 3a 



2 dy \ 1 1 1 



therefore - -/ = - H 1 



y ax x x a x 



dj _ 1 (x (x a) (x 2a)| 

 dx 2 1 



(i); 



r r + -^+ - f 



) [x x a x i 

 Also from (1) we have 



y= x(l-^(l-^-(l + -}' k - 



(2). 



_ I | | *~ _ "" )\1 ill 



27q* 



BB2 



