Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Результати 1-5 із 51
Сторінка 15
... 1.2 ( nr + 1 ) ( n − r + 2 ) u1 r ( r - 1 ) си 1. ( nr + 1 ) u ' " + & c . } ( A ) * Mémoires de Berlin , 1772 , p . 213 . By developing in a different manner a more convenient formula SUCCESSIVE DIFFERENTIATION . 15.
... 1.2 ( nr + 1 ) ( n − r + 2 ) u1 r ( r - 1 ) си 1. ( nr + 1 ) u ' " + & c . } ( A ) * Mémoires de Berlin , 1772 , p . 213 . By developing in a different manner a more convenient formula SUCCESSIVE DIFFERENTIATION . 15.
Сторінка 16
D. F. Gregory. By developing in a different manner a more convenient formula may be obtained : ( n + h + ch ) " = " ( 1 + = u ' u " { ( 1 + h ) 2 + 2u 4ис - u ' h + h2 ) " u ገ 4u2 и But 4uc u'2 = 4ac - b2 = e2 suppose . - Developing u ...
D. F. Gregory. By developing in a different manner a more convenient formula may be obtained : ( n + h + ch ) " = " ( 1 + = u ' u " { ( 1 + h ) 2 + 2u 4ис - u ' h + h2 ) " u ገ 4u2 и But 4uc u'2 = 4ac - b2 = e2 suppose . - Developing u ...
Сторінка 17
... formula ( B ) , d " ( a2 + x2 ) " dx " + = = = 2x , e = 4a2 , and if we make r = n , we find by 2n ( 2n − 1 ) ... ( n + 1 ) x ” { 1 + - { n ( n − 1 ) } 2 ( n − 2 ) ( n − 3 ) a1 - - x1 n2 n - 1 a2 --- 1 2n ( 2n - 1 ) x2 1.2 2n ... ( 2n ...
... formula ( B ) , d " ( a2 + x2 ) " dx " + = = = 2x , e = 4a2 , and if we make r = n , we find by 2n ( 2n − 1 ) ... ( n + 1 ) x ” { 1 + - { n ( n − 1 ) } 2 ( n − 2 ) ( n − 3 ) a1 - - x1 n2 n - 1 a2 --- 1 2n ( 2n - 1 ) x2 1.2 2n ... ( 2n ...
Сторінка 18
... formula ( B ) , 3.4 ... ( + 1 ) -1 d'u da ( 1 - a2 ) + 3 ( 1 ) ( - 2 ) 1 - 3.4 3.5 ( r− 1 ) ( r− 2 ) ( r − 3 ) ( r − 4 ) 1 2.4 3 4 5.6 . x du ( 23 ) u = sin -1 = a dx 1 ( a2 - x2 ) + & c . } ď u dx = = dr - 1 1 dx ...
... formula ( B ) , 3.4 ... ( + 1 ) -1 d'u da ( 1 - a2 ) + 3 ( 1 ) ( - 2 ) 1 - 3.4 3.5 ( r− 1 ) ( r− 2 ) ( r − 3 ) ( r − 4 ) 1 2.4 3 4 5.6 . x du ( 23 ) u = sin -1 = a dx 1 ( a2 - x2 ) + & c . } ď u dx = = dr - 1 1 dx ...
Сторінка 20
... formula d'u dx = c ( - ) * ‚ 2 { ( − ) 3 ( 2x ) ' + ( − ) ' = ' r ( r − 1 ) ( 2a ) * - * -- - - + ( − ) ' = ' ' ? ' ( ' − 1 ) ... ( r ' − 3 ) 2 - 1.2 Now generally ( - ) = c ( − ) * » } , and ( - ) * ( - ) = COS ( x2 + p π ...
... formula d'u dx = c ( - ) * ‚ 2 { ( − ) 3 ( 2x ) ' + ( − ) ' = ' r ( r − 1 ) ( 2a ) * - * -- - - + ( − ) ' = ' ' ? ' ( ' − 1 ) ... ( r ' − 3 ) 2 - 1.2 Now generally ( - ) = c ( − ) * » } , and ( - ) * ( - ) = COS ( x2 + p π ...
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