Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 6-10 із 59
Сторінка 90
... easily scen . ( 39 ) If a u = 2 * sin find its value when a = This function may be put under the form በ sin በ Q4 a which , if = 0 , becomes a 2 sin 0 Ꮎ When = 0 , 0 = 0 , and sin 0 Ꮎ 1 , ( 40 ) Let n = and therefore u = a . ( a2 ...
... easily scen . ( 39 ) If a u = 2 * sin find its value when a = This function may be put under the form በ sin በ Q4 a which , if = 0 , becomes a 2 sin 0 Ꮎ When = 0 , 0 = 0 , and sin 0 Ꮎ 1 , ( 40 ) Let n = and therefore u = a . ( a2 ...
Сторінка 103
... easily seen that the area of the triangle ACX is proportional to ax , and that of a ( b - x ) 2 BXY to 00 a { x + so that we have - ( b − x ) 2 ) 00 - a minimum . 2 = Whence we find 2 b2 = 0 , or a b3 , which determines the line CXY ...
... easily seen that the area of the triangle ACX is proportional to ax , and that of a ( b - x ) 2 BXY to 00 a { x + so that we have - ( b − x ) 2 ) 00 - a minimum . 2 = Whence we find 2 b2 = 0 , or a b3 , which determines the line CXY ...
Сторінка 110
... easily expressed , and as such functions rarely if ever occur in practice , it is unnecessary to give it here . Français has shewn that in a function of two variables , when the equations du da = 0 , du dy - 0 , are satisfied ...
... easily expressed , and as such functions rarely if ever occur in practice , it is unnecessary to give it here . Français has shewn that in a function of two variables , when the equations du da = 0 , du dy - 0 , are satisfied ...
Сторінка 116
... easily find ( 9 ) x = y = 8 = 13 and u = π , Find the maximum value of u = al + bm + cn , a maximum . l , m , n being variable and subject to the condition 12 + m2 + n2 = 1 . We easily find by the use of an indeterminate multiplier that ...
... easily find ( 9 ) x = y = 8 = 13 and u = π , Find the maximum value of u = al + bm + cn , a maximum . l , m , n being variable and subject to the condition 12 + m2 + n2 = 1 . We easily find by the use of an indeterminate multiplier that ...
Сторінка 117
... easily find x = y = x = a , so that the surface equals 6a2 , a minimum . ( 12 ) To inscribe the greatest rectangular parallelopiped in a given ellipsoid . Let the equation to the ellipsoid be + + = ; 2 aa b ? and let x , y , ≈ be the ...
... easily find x = y = x = a , so that the surface equals 6a2 , a minimum . ( 12 ) To inscribe the greatest rectangular parallelopiped in a given ellipsoid . Let the equation to the ellipsoid be + + = ; 2 aa b ? and let x , y , ≈ be the ...
Інші видання - Показати все
Загальні терміни та фрази
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