Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 44
Сторінка 22
... negative indices must disappear of themselves . Hence taking the terms with positive indices only ( - ( e + 1 ) +1 . d u dxr = ( r + 1 ) r + { 3r 2 * + 1.2 ( r + 1 ) ~ 1r } e ( r − 2 ) x + & c . ] and therefore ď u dx r - 1 ...
... negative indices must disappear of themselves . Hence taking the terms with positive indices only ( - ( e + 1 ) +1 . d u dxr = ( r + 1 ) r + { 3r 2 * + 1.2 ( r + 1 ) ~ 1r } e ( r − 2 ) x + & c . ] and therefore ď u dx r - 1 ...
Сторінка 61
... the first of these values , we find the series 203 - x5 & c . u = - Taking the positive value of a , u = α- x2 Ꮖ 3 x3 + 2 8 a 16a2 ' & c . Taking the negative value of a , a x02 5003 u = -at + & c . 2 8 a 8 a * ( 13 ) If sin y = x sin ( ...
... the first of these values , we find the series 203 - x5 & c . u = - Taking the positive value of a , u = α- x2 Ꮖ 3 x3 + 2 8 a 16a2 ' & c . Taking the negative value of a , a x02 5003 u = -at + & c . 2 8 a 8 a * ( 13 ) If sin y = x sin ( ...
Сторінка 66
... negative powers the result gives us the sum of the nth negative powers of the roots ; while , as has just been stated , the whole series gives the nth negative power of the least root . ( 9 ) If the equation be - cy2 — by + a = of which ...
... negative powers the result gives us the sum of the nth negative powers of the roots ; while , as has just been stated , the whole series gives the nth negative power of the least root . ( 9 ) If the equation be - cy2 — by + a = of which ...
Сторінка 74
... negative according as ( n − 1 ) r is even or odd . When n is odd the second series terminates ; when n is even it continues to infinity . When n is fractional both series coexist , except for particular values of r . ( 8 ) To expand ...
... negative according as ( n − 1 ) r is even or odd . When n is odd the second series terminates ; when n is even it continues to infinity . When n is fractional both series coexist , except for particular values of r . ( 8 ) To expand ...
Сторінка 88
... negative , u∞ . 1 ( 32 ) u = u = 1 - Ꮖ 1 + x 2 - 1 - x2 2 - - 002 0 - 0 = = 1 - - ∞ , when a = 1 . , when a = 1 . ( 33 ) u = u = x X- 1 x log x - 1 log x = x + 1 ( x - 1 ) log x ( 34 ) The sum of the series 8 = 0 0 - ∞ , when x = 1 ...
... negative , u∞ . 1 ( 32 ) u = u = 1 - Ꮖ 1 + x 2 - 1 - x2 2 - - 002 0 - 0 = = 1 - - ∞ , when a = 1 . , when a = 1 . ( 33 ) u = u = x X- 1 x log x - 1 log x = x + 1 ( x - 1 ) log x ( 34 ) The sum of the series 8 = 0 0 - ∞ , when x = 1 ...
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a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³