Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 79
Сторінка 16
... multiply h ' , we find that the term in ( u + u'h ) " is n ( n − 1 ) ... ( n − r + 1 ) u " - u ' ' ; ... in ( u + ... multiplying by 1.2 ... r , obtain for the 7th differential coefficient of u " we d ( v " ) = n ( n dx ' + - - 1 ) ...
... multiply h ' , we find that the term in ( u + u'h ) " is n ( n − 1 ) ... ( n − r + 1 ) u " - u ' ' ; ... in ( u + ... multiplying by 1.2 ... r , obtain for the 7th differential coefficient of u " we d ( v " ) = n ( n dx ' + - - 1 ) ...
Сторінка 17
... multiplied by 1.2 ... r . Now expanding each term by the binomial theorem , we have for the coefficient of h ' in ... multiplying by 1.2 ... r , we find ď ' ( u " ) • r n · = 2n ( 2n − 1 ) ... ( 2n - r ÷ 1 ) u " - " { 1+ r ( r − 1 ) e2 ...
... multiplied by 1.2 ... r . Now expanding each term by the binomial theorem , we have for the coefficient of h ' in ... multiplying by 1.2 ... r , we find ď ' ( u " ) • r n · = 2n ( 2n − 1 ) ... ( 2n - r ÷ 1 ) u " - " { 1+ r ( r − 1 ) e2 ...
Сторінка 20
... Multiplying these together , taking only the coefficient of h ' , and multiplying it by 1.2 ... r , we find d u dx " = + { c ' ( 2x ) ' + r ( r − 1 ) cr − 1 ( 2x ) ′′ - 2 r ( r− 1 ) ... ( r − 3 ) 1.2 - cr - 2 ( 2x ) ” − 1 + & c ...
... Multiplying these together , taking only the coefficient of h ' , and multiplying it by 1.2 ... r , we find d u dx " = + { c ' ( 2x ) ' + r ( r − 1 ) cr − 1 ( 2x ) ′′ - 2 r ( r− 1 ) ... ( r − 3 ) 1.2 - cr - 2 ( 2x ) ” − 1 + & c ...
Сторінка 22
... multiplying by ( +1 ) +1 we must have ( r - 1 ) x + & c . + a1 € * ( 1 ) . d'u ( ε * + 1 ) +1 = dxr Now as u = € -2x - 3r 6 + € - ď u -2x - dx - & c . -3r - = ( − ) ′ { 1 ′ e ̄ * − 2′e ̄2 * + 3 ′ e ̃33 − 4 ′ € ̄1 * + & c . } ...
... multiplying by ( +1 ) +1 we must have ( r - 1 ) x + & c . + a1 € * ( 1 ) . d'u ( ε * + 1 ) +1 = dxr Now as u = € -2x - 3r 6 + € - ď u -2x - dx - & c . -3r - = ( − ) ′ { 1 ′ e ̄ * − 2′e ̄2 * + 3 ′ e ̃33 − 4 ′ € ̄1 * + & c . } ...
Сторінка 44
... Multiplying the former by 2 and adding , d v + p2 y = 0 . dx2 ( 6 ) Eliminate m and a from the equation - y2 = m ( a2 − x2 ) ; the result is ď y xy + x da dy dy = 0 . -y dx dx - y = ce i - y . ( 7 ) Eliminate e from the equation x - y ...
... Multiplying the former by 2 and adding , d v + p2 y = 0 . dx2 ( 6 ) Eliminate m and a from the equation - y2 = m ( a2 − x2 ) ; the result is ď y xy + x da dy dy = 0 . -y dx dx - y = ce i - y . ( 7 ) Eliminate e from the equation x - y ...
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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