12 



TABLE 5. 

 DIFFERENTIAL COEFFICIENTS. 



INTEGRALS. 



Taylor's series : 



u=f(x+h)=f(x) +f'(x)h+f"(x) ^ +/'"( 



The remainder after the first w terms is expressed by 



f n f n+l (x+h-z)z*.dz. 



I.2. 3 



Maclaurin's series : 



u=f(x)=f(o)+f'(o)x+f"(o) ~ 



^=3.14159265359 

 i =0.3 1 83098861 8 



^=9.86960440109 

 ^=2.71828182846 



=0.497 1 4987 269 



^=0.88622692546 



log e 10=2.30258509299 



log^(number) =log e (number) logs e 

 _ log ff (number) 

 log e J5 



SMITHSONIAN TABLES. 



