Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 50
Сторінка 14
... expanding ď ( uv ) dx " d ' ( uv ) dx * r by the Theorem of Leibnitz , = € ar ( a2 + n2 ) 2 [ x TM cos ( nx + r p ) -1 + r.mx- cos { nx + ( r− 1 ) 4 } ( a2 + n2 ) } r ( r− 1 ) - m ( m − 1 ) xm - 2 2 1.2 cos { nx + ( r− 2 ) p } ( a2 ...
... expanding ď ( uv ) dx " d ' ( uv ) dx * r by the Theorem of Leibnitz , = € ar ( a2 + n2 ) 2 [ x TM cos ( nx + r p ) -1 + r.mx- cos { nx + ( r− 1 ) 4 } ( a2 + n2 ) } r ( r− 1 ) - m ( m − 1 ) xm - 2 2 1.2 cos { nx + ( r− 2 ) p } ( a2 ...
Сторінка 16
... expanding each term by the binomial theorem , we have for the coefficient of u ' ' 1 2n ( 2n - 1 ) ... ( 2nr + 1 ) h ' in the first term 2 1.2 ... r T - 2 1 - ( 2n − 2 ) ... ( 2n − r + 1 ) n - second e2 , 22 u 1.2 ... ( r2 ) r - 4 и ...
... expanding each term by the binomial theorem , we have for the coefficient of u ' ' 1 2n ( 2n - 1 ) ... ( 2nr + 1 ) h ' in the first term 2 1.2 ... r T - 2 1 - ( 2n − 2 ) ... ( 2n − r + 1 ) n - second e2 , 22 u 1.2 ... ( r2 ) r - 4 и ...
Сторінка 20
... r + & c . 1 ( 27 ) Let u = € + 1 We might in this case expand the function and differen- tiater times each term in the development , but as this would give d'u dx expressed in an infinite series , 20 SUCCESSIVE DIFFERENTIATION .
... r + & c . 1 ( 27 ) Let u = € + 1 We might in this case expand the function and differen- tiater times each term in the development , but as this would give d'u dx expressed in an infinite series , 20 SUCCESSIVE DIFFERENTIATION .
Сторінка 26
... expanded not homogeneous . x ( 19 ) Let u = y3 + x3 y -x Then n = 2 and 2 ( y3 + x3 ) - du x- dx du + y dy ( 20 ) u = du dx + y du dy = 2y1 - 2y3 x + 2y x3 − 2 x1 x + y1 = x + y - ( y = x ) 2 y -x Then n = - , and ( x + y ) = ( x + y ) ...
... expanded not homogeneous . x ( 19 ) Let u = y3 + x3 y -x Then n = 2 and 2 ( y3 + x3 ) - du x- dx du + y dy ( 20 ) u = du dx + y du dy = 2y1 - 2y3 x + 2y x3 − 2 x1 x + y1 = x + y - ( y = x ) 2 y -x Then n = - , and ( x + y ) = ( x + y ) ...
Сторінка 27
... expanded in terms of a so as to be of the form Σ . ( Q ; x1y " -i ) , Σ then will { ( 2i — n ) Q ; } = 0 . - As u is ... expansion of u in this equation , we get Σ { ( 2i − n ) Q ; x " } - i = 0 , or Σ { ( 2i – n ) Q ; } = 0 . • This ...
... expanded in terms of a so as to be of the form Σ . ( Q ; x1y " -i ) , Σ then will { ( 2i — n ) Q ; } = 0 . - As u is ... expansion of u in this equation , we get Σ { ( 2i − n ) Q ; x " } - i = 0 , or Σ { ( 2i – n ) Q ; } = 0 . • This ...
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a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx 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 radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³