Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 100
Сторінка 14
... Whence , comparing these expressions , it appears that ( de ) dx T d 22 ax = ar ― n x2 - r ax dx ( 15 ) d ' ( uv ) dx uv = x " log x , = n ( n − 1 ) ... ( n − r + 1 ) x ” -r { log a + r r ( r - 1 ) 1 2 r ( r− 1 ) ( r− 2 ) 1 - ( n ...
... Whence , comparing these expressions , it appears that ( de ) dx T d 22 ax = ar ― n x2 - r ax dx ( 15 ) d ' ( uv ) dx uv = x " log x , = n ( n − 1 ) ... ( n − r + 1 ) x ” -r { log a + r r ( r - 1 ) 1 2 r ( r− 1 ) ( r− 2 ) 1 - ( n ...
Сторінка 15
... Whence it appears that d ) x = € + a dx a ) -ar ax ( " * X ) . dx This result , when generalized , is of great importance in the solution of Differential Equations . If the function to be differentiated be ( a + SUCCESSIVE ...
... Whence it appears that d ) x = € + a dx a ) -ar ax ( " * X ) . dx This result , when generalized , is of great importance in the solution of Differential Equations . If the function to be differentiated be ( a + SUCCESSIVE ...
Сторінка 37
... r d R cos 0 sin 0 + dr ᏧᎾ T dx dR dy = = dR * Lagrange , Mémoires de Berlin , 1773 , p . 121 . Legendre , Mémoires de l'Académie des Sciences , 1788 , p . 454 . dR dR d R whence c -y dy Y da CHANGE OF THE INDEPENDENT VARIABLE . 37.
... r d R cos 0 sin 0 + dr ᏧᎾ T dx dR dy = = dR * Lagrange , Mémoires de Berlin , 1773 , p . 121 . Legendre , Mémoires de l'Académie des Sciences , 1788 , p . 454 . dR dR d R whence c -y dy Y da CHANGE OF THE INDEPENDENT VARIABLE . 37.
Сторінка 38
... Whence Φφ = dx2 dy dr2 dr \ r Ф dr2 and therefore This equation occurs in researches on the motion of fluids . 1 do + = 0 . r dr ( 4 ) If + ď o dx2 ď ď p . Φ dy2 dx2 = 0 , we find when x2 + y2 + s3 = p2 38 CHANGE OF THE INDEPENDENT ...
... Whence Φφ = dx2 dy dr2 dr \ r Ф dr2 and therefore This equation occurs in researches on the motion of fluids . 1 do + = 0 . r dr ( 4 ) If + ď o dx2 ď ď p . Φ dy2 dx2 = 0 , we find when x2 + y2 + s3 = p2 38 CHANGE OF THE INDEPENDENT ...
Сторінка 44
... whence y - B x- d'y dey da 313 dx2 dr2 Substituting these values of yẞ and a - a , we have 1 + 213 dy dx dy dx2 2 - p2 , in which a and ẞ no longer appear . This is the expression for the square of the radius 44 ELIMINATION OF CONSTANTS ...
... whence y - B x- d'y dey da 313 dx2 dr2 Substituting these values of yẞ and a - a , we have 1 + 213 dy dx dy dx2 2 - p2 , in which a and ẞ no longer appear . This is the expression for the square of the radius 44 ELIMINATION OF CONSTANTS ...
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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