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 65
... equation either algebraic or transcendental , and Lagrange has shown that the series always gives the least root of the equation . ( 6 ) Let y3 - ay + b = 0 : expand y " in terms of - . a Here ƒ ( x ) = x ” , b $ ( x ) = x3 , ≈ = a ...
... equation either algebraic or transcendental , and Lagrange has shown that the series always gives the least root of the equation . ( 6 ) Let y3 - ay + b = 0 : expand y " in terms of - . a Here ƒ ( x ) = x ” , b $ ( x ) = x3 , ≈ = a ...
Сторінка 66
... Let 1 - y + ae3 = 0 : expand y " in terms of a , a1 + & c . n ( n + 1 ) y ... equation y = x + x + ( y ) , of % , and if we only retain the terms ... equation be - cy2 — by + a = of which the two roots are a , ẞ , then 1 + = a 4 - nc ...
... Let 1 - y + ae3 = 0 : expand y " in terms of a , a1 + & c . n ( n + 1 ) y ... equation y = x + x + ( y ) , of % , and if we only retain the terms ... equation be - cy2 — by + a = of which the two roots are a , ẞ , then 1 + = a 4 - nc ...
Сторінка 67
Duncan Farquharson Gregory. ( 10 ) Let a - by + cy " = 0 . Then if we represent ... equation , we obtain a series for the direct th powers of the roots of the ... Let u = m + e sin u . Expand u and sinu in terms of e . The expression for u ...
Duncan Farquharson Gregory. ( 10 ) Let a - by + cy " = 0 . Then if we represent ... equation , we obtain a series for the direct th powers of the roots of the ... Let u = m + e sin u . Expand u and sinu in terms of e . The expression for u ...
Сторінка 71
... equation , in Therefore , forming the successive = = € . = which case do coefficients from this first one , 2x2 5003 + e " = e { 1 + x + + 1.2 151 52x5 1.2.3 1.2.3.4 1.2.3.4.5 + + & c . } . ( 2 ) Let u = 6 sin x the co- Then by the same ...
... equation , in Therefore , forming the successive = = € . = which case do coefficients from this first one , 2x2 5003 + e " = e { 1 + x + + 1.2 151 52x5 1.2.3 1.2.3.4 1.2.3.4.5 + + & c . } . ( 2 ) Let u = 6 sin x the co- Then by the same ...
Сторінка 115
... equation in k P mum value may be found . " - whence a maximum and a mini- This is the equation for determining the radii of maximum and minimum curvature in a curved surface . ( 6 ) Let u = ay ( c − x ) = b≈ ( a − x ) = cx ( b − y ) ...
... equation in k P mum value may be found . " - whence a maximum and a mini- This is the equation for determining the radii of maximum and minimum curvature in a curved surface . ( 6 ) Let u = ay ( c − x ) = b≈ ( a − x ) = cx ( b − 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