96 EXAMPLES OF THE EXPANSION OF FUNCTIONS. 



Bernoulli, having been first noticed by James Bernoulli. It 

 will be found that 



7? 7? 7? JL 7? P 



** 6' 3 ~30' 8 ~42' 7 ~30' 9 ~66'"* 



EXAMPLES. 



1. If e 2 * (3 x) xe* x3 be expanded by Maclaurin's 



4 x 5 

 Theorem, the first term is -pr- . 



L2 



2. Expand log (1 + e*} in powers of #. 



Result. log2 



3. Expand e"*** in powers of x. 



Result. 





 4. e* sec a; = 1 + # + x + - + . . . 



8 



a 



C. 



7. 



8. 



16xl7a; 8 



-log cos x = + - + -+-- 



-f 4 



11. sin- (x + 1) = sin-'* + -A + 





