Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 60
Сторінка 99
... of the problem , To find the height at which a light should be placed so that a small plane surface at a given horizontal distance shall receive the greatest illumination from it . ( 11 ) u = x = ( ab ) 7-2 MAXIMA AND MINIMA . 99.
... of the problem , To find the height at which a light should be placed so that a small plane surface at a given horizontal distance shall receive the greatest illumination from it . ( 11 ) u = x = ( ab ) 7-2 MAXIMA AND MINIMA . 99.
Сторінка 104
... surface . = ( 29 ) The content of a cone being given , find its form when the surface is a maximum . Let πα 3 be the given content , the radius of the base , y the height of the cone . the cone of greatest surface . α Then x = 23 , y ...
... surface . = ( 29 ) The content of a cone being given , find its form when the surface is a maximum . Let πα 3 be the given content , the radius of the base , y the height of the cone . the cone of greatest surface . α Then x = 23 , y ...
Сторінка 105
... surface is visible . If r , be the radii of the spheres , a the distance of the centres , and the distance of the required point from the centre of the sphere whose radius is r . Then x = art ri + r'i ' ( 32 ) A regular hexagonal prism ...
... surface is visible . If r , be the radii of the spheres , a the distance of the centres , and the distance of the required point from the centre of the sphere whose radius is r . Then x = art ri + r'i ' ( 32 ) A regular hexagonal prism ...
Сторінка 106
... surface , and he requested Koenig to examine the question mathematically . That geome- ter confirmed the conjecture ; -the result of his calculations agreeing with Maraldi's measurements within 2 ' . Maclaurin † and L'Huilliert , by ...
... surface , and he requested Koenig to examine the question mathematically . That geome- ter confirmed the conjecture ; -the result of his calculations agreeing with Maraldi's measurements within 2 ' . Maclaurin † and L'Huilliert , by ...
Сторінка 115
... surface . ( 6 ) Let u = ay ( c − x ) = b≈ ( a − x ) = cx ( b − y ) . Then a = a , y = 1b , c , give 1 ૢ % = u = abc , a maximum . ( 7 ) Let u = a cos2x + b cos❜y ; - - r and y being subject to the condition y − x = π ...
... surface . ( 6 ) Let u = ay ( c − x ) = b≈ ( a − x ) = cx ( b − y ) . Then a = a , y = 1b , c , give 1 ૢ % = u = abc , a maximum . ( 7 ) Let u = a cos2x + b cos❜y ; - - r and y being subject to the condition y − x = π ...
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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