1J ANALYTIC GBOMSTRY [Ce. L 



then TJ grows smaller and x, grows larger; and if c = 0,* 

 tlim jr l = 0, while , = -- 



: a remains nnrhan^'d while e = and b = 0, then 

 jjj - and x, = 0. 



/. ami / remain unehan^ed whilt^ a= 0, then ar,= 

 and ./. : Incomes infinitely large. 



( i .-mains unrhanijed wliile a = and 6 = 0, thru 



/j a i id j- 3 become infinitely large. 



a and c ivmain unclian^ed \vliik- I = 0, thru 



undent should translate (1), (2), (3), ( I), and (6) 

 into more general terms by reading "the absolut. t,-rm 

 approaches zero as a limit" instead of "c = 0," etc. 



11. Properties of the quadratic equation. By adding tli> 

 two roots of 



and also multiplying them together, the relations 



b 



:!...< 



a a 



are obtained; or, if equation (1) is written with the coeffi- 

 cient of the term of the sri-nlld degree Ted I lei M 1 to IlllitV, OS 



j- + px + q = 0, 

 these relations become 



Or, expressed in words: the coefficient of the term of tin: 

 second degree being unity, the coefficient of the term of 



The sign = is read " approaches as a limit. 1 ' It was introduced b;. 

 late 1'rofessor Oliver of Cornell University. 



