DIFFERENTIAL CALCULUS. 197 



933. In the equation 

 /(a + h) ./() 



the limiting value of 0, when h is indefinitely diminished, is 

 TJ and, if/(x) be a rational algebraical expression of n+ 1 



dimensions in x, the value of is always -- - . 



93 i. In the equation 



F(x + k)- F(x) F*(x + $h) 



that 6 will be constant if F(X) = BIUX and f (x) = cos x. 

 also that, in all cases, the limiting value of 0, when h is 

 indefinitely diminished, is . 



935. Trove that 



c'-l 1 1 1 



an.l that 



93C. Trove that 



, .JI + JS+ ...-f 



1 + 2"^ s" 1 - * w > 



/' hin (;/ ^ l) tt 



O06a+oo82a-f...-fco8fia< >- -1: 



a a 



na in the last being * 



7. Ify = xco^v ' trnn of the -n of 



in terms of 

 / 1 \ -< + 





