Examples of the Processes of the Differential and Integral Calculus |
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Page 15
... obtain ( u + b ) + n ( u + h ) n - ch ° + n ( n 1 ) ( u + u'h ) " - 2 c2h ++ & c . 1.2 Again , developing each binomial and taking only the terms which multiply h ' , we find that the term in ... 1.2 ( u + u'h ) " is n ( n - 1 ) ( n in ...
... obtain ( u + b ) + n ( u + h ) n - ch ° + n ( n 1 ) ( u + u'h ) " - 2 c2h ++ & c . 1.2 Again , developing each binomial and taking only the terms which multiply h ' , we find that the term in ... 1.2 ( u + u'h ) " is n ( n - 1 ) ( n in ...
Page 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 ...
Page 50
... obtain as the result of the elimination of the functions a2 - da 1 ( d ) " } - b2 Jd2 ≈ \ dy 2 2 - 2 dz = 0 . y ( 23 ) Eliminate the arbitrary functions from ( 1 ) xf ( a ) + yp ( a ) + ≈ √ ( a ) = 1 , where a is a function of a , y ...
... obtain as the result of the elimination of the functions a2 - da 1 ( d ) " } - b2 Jd2 ≈ \ dy 2 2 - 2 dz = 0 . y ( 23 ) Eliminate the arbitrary functions from ( 1 ) xf ( a ) + yp ( a ) + ≈ √ ( a ) = 1 , where a is a function of a , y ...
Page 67
... obtain a series for the direct th powers of the roots of the original equation . ( 11 ) If we thus transform the equation in Ex . 10 , it becomes c - by + ay2 = 0 ; and if a , ẞ be the same quantities as before , ca n ( n = 3 ) c2 a2 a2 ...
... obtain a series for the direct th powers of the roots of the original equation . ( 11 ) If we thus transform the equation in Ex . 10 , it becomes c - by + ay2 = 0 ; and if a , ẞ be the same quantities as before , ca n ( n = 3 ) c2 a2 a2 ...
Page 73
... Every term on the second side vanishes except the first , and there remains a = cos n ( 2r + 1 ) — · To find a1 , make x = ( 2r + 1 ) — in the second equation , when we obtain 2 π sin n ( 2 + 1 ) 2 π DEVELOPMENT OF FUNCTIONS . 73.
... Every term on the second side vanishes except the first , and there remains a = cos n ( 2r + 1 ) — · To find a1 , make x = ( 2r + 1 ) — in the second equation , when we obtain 2 π sin n ( 2 + 1 ) 2 π DEVELOPMENT OF FUNCTIONS . 73.
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