196 BOOK OF MATHEMATICAL PROBLEMS. 



928. Having given 



y S {* 

 prove that 



929. If 



sin (m ttM~ l x) 

 prove that 



(n + 1 ) (n + 2) a m+ , -f (2w + m 9 ) a m + (n - 1 ) (n - 2) a n _ , = 0. 



930. If 

 then will 



1 1 



931. In the equation 



/(* + K) ./() 



the limiting value of ^, when A is indefinitely diminished, is ; 

 and, if 6 be constant, /(#)= ^ + ^ -f Cx* t where J, ^, C are in- 

 dependent of x. 



932. In the equation 



prove that the first two terms of the expansion of in ascending 

 powers of h are 



1 , A /"(). 

 + ' 



and, if /(x) = sin #, the first three terms of the expansion are 



1 A c 



2 * ~~2 



provided that cot x be finite. 



1 A cot a; A* 



2 * ~~24~ ~ 48 sin 8 x ' 



