Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 51
Сторінка 15
... ) ( rs ) cu2 1.2 ( nr + 1 ) ( n − r + 2 ) u'1 * r ( r - 1 ) cu 1. ( n − r + 1 ) u ' * + & c . } ( A ) * Mémoires de Berlin , 1772 , p . 213 . By developing in a different manner a more convenient formula SUCCESSIVE DIFFERENTIATION . 15.
... ) ( rs ) cu2 1.2 ( nr + 1 ) ( n − r + 2 ) u'1 * r ( r - 1 ) cu 1. ( n − r + 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
Duncan Farquharson Gregory William Walton. By developing in a different manner a more convenient formula may be obtained : ( u + h + ch ) = u " ( 1 + κ ' = u " { ( 1 + 22 = h ) 2 + But 4uc -U u'2 = 4ac Developing u " { ( 1 + theorem , we ...
Duncan Farquharson Gregory William Walton. By developing in a different manner a more convenient formula may be obtained : ( u + h + ch ) = u " ( 1 + κ ' = u " { ( 1 + 22 = h ) 2 + But 4uc -U u'2 = 4ac Developing u " { ( 1 + theorem , we ...
Сторінка 17
... formula ( B ) , d " ( a2 + x2 ) " dx " = · 2n ( 2n − 1 ) ... ( n + 1 ) ∞ ” { 1 + - n - 1 a2 2n ( 2n - 1 ) x2 3 ) 201 + & c . } . { n ( n − 1 ) } 2 ( n − 2 ) ( n − 3 ) a1 - 1.2 2n ... ( 2n - 3 ) ( 20 ) Let u = 1 a2 + x2 The 7th ...
... formula ( B ) , d " ( a2 + x2 ) " dx " = · 2n ( 2n − 1 ) ... ( n + 1 ) ∞ ” { 1 + - n - 1 a2 2n ( 2n - 1 ) x2 3 ) 201 + & c . } . { n ( n − 1 ) } 2 ( n − 2 ) ( n − 3 ) a1 - 1.2 2n ... ( 2n - 3 ) ( 20 ) Let u = 1 a2 + x2 The 7th ...
Сторінка 18
... formula ( B ) , d'u 3.4 ... ( + 1 ) -1 = dx ( 1 − ∞2 ) TM + } { 1+ - 3 ( r− 1 ) ( r− 2 ) 1 2 - 3.4 3. 5 ( r − 1 ) ( r − 2 ) ( r − 3 ) ( r − 4 ) 1 2.4 - - 3.4 5.6 + & c . } x4 -12 x du ( 23 ) u = sin -1 = a dx ( a2 ...
... formula ( B ) , d'u 3.4 ... ( + 1 ) -1 = dx ( 1 − ∞2 ) TM + } { 1+ - 3 ( r− 1 ) ( r− 2 ) 1 2 - 3.4 3. 5 ( r − 1 ) ( r − 2 ) ( r − 3 ) ( r − 4 ) 1 2.4 - - 3.4 5.6 + & c . } x4 -12 x du ( 23 ) u = sin -1 = a dx ( a2 ...
Сторінка 20
... formula ďu = c ( - ) * a2 { ( − ) 13 ( 2x ) ' + ( − ) ' = ' r ( r − 1 ) ( 2.x ) r - 2 dx = + ( - ) ' ï32 r ( r − 1 ) ... ( r − 3 ) 1.2 Now generally ( - ) = c ( − ) * p 7 , and c ( - ) * 2 ( - ) * p ! = COS ( 2x ) ' 1 + & c . } ...
... formula ďu = c ( - ) * a2 { ( − ) 13 ( 2x ) ' + ( − ) ' = ' r ( r − 1 ) ( 2.x ) r - 2 dx = + ( - ) ' ï32 r ( r − 1 ) ... ( r − 3 ) 1.2 Now generally ( - ) = c ( − ) * p 7 , and c ( - ) * 2 ( - ) * p ! = COS ( 2x ) ' 1 + & c . } ...
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³