Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
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Сторінка v
... first place , on considering the subject , I could find no arguments against the use of the notation for Dif- ferentials , which did not apply with even greater force against that for integrals : indeed , although there may be some ...
... first place , on considering the subject , I could find no arguments against the use of the notation for Dif- ferentials , which did not apply with even greater force against that for integrals : indeed , although there may be some ...
Сторінка vi
... as great an extent as I wished , but these digressions short as they are may serve to relieve the dryness of a mere collection of Examples . TRINITY COLLEGE , October , 1841 . EDITOR'S NOTICE . THE first edition of this work , vi PREFACE .
... as great an extent as I wished , but these digressions short as they are may serve to relieve the dryness of a mere collection of Examples . TRINITY COLLEGE , October , 1841 . EDITOR'S NOTICE . THE first edition of this work , vi PREFACE .
Сторінка vii
Duncan Farquharson Gregory. EDITOR'S NOTICE . THE first edition of this work , which appeared at the close of the year 1841 , having been exhausted , a new edition is , under the sanction of the Proprietors , now presented to the public ...
Duncan Farquharson Gregory. EDITOR'S NOTICE . THE first edition of this work , which appeared at the close of the year 1841 , having been exhausted , a new edition is , under the sanction of the Proprietors , now presented to the public ...
Сторінка 16
... first degree , as into ( x + a ) ( x + ẞ ) , and then differentiating the product ( x + a ) " ( x + B ) " by the Theorem of Leibnitz ; but instead of doing so we shall make use of two formulæ given by Lagrange * . Let u = a + bx + cx2 ...
... first degree , as into ( x + a ) ( x + ẞ ) , and then differentiating the product ( x + a ) " ( x + B ) " by the Theorem of Leibnitz ; but instead of doing so we shall make use of two formulæ given by Lagrange * . Let u = a + bx + cx2 ...
Сторінка 17
... of h ' in the first term u - 9 second ... 9 third ... 1 2n ( 2n − 1 ) ... ( 2n − r + 1 ) ̧ u * T - 2 1.2 ... r 1 ( 2n - 2 ) ... ( 2n - r + 1 ) n 2 * u * . e2 , 1.2 ... ( r - 2 ) 1 u \ " -4 1 ( 2n - 4 ) ... ( 2n − r + 1 ) n ( n ...
... of h ' in the first term u - 9 second ... 9 third ... 1 2n ( 2n − 1 ) ... ( 2n − r + 1 ) ̧ u * T - 2 1.2 ... r 1 ( 2n - 2 ) ... ( 2n - r + 1 ) n 2 * u * . e2 , 1.2 ... ( r - 2 ) 1 u \ " -4 1 ( 2n - 4 ) ... ( 2n − r + 1 ) n ( n ...
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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