Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 6-10 із 61
Сторінка 65
... preceding examples it will be seen that the expan- sion of y in terms of b is the solution of an equation either algebraic or transcendental , and Lagrange has shewn that the series always gives the least root of the equation . ( 6 ) ...
... preceding examples it will be seen that the expan- sion of y in terms of b is the solution of an equation either algebraic or transcendental , and Lagrange has shewn that the series always gives the least root of the equation . ( 6 ) ...
Сторінка 69
... by particular methods . The preceding Theorems sometimes fail from the function which is to be expanded becoming infinite or indeterminate for particular values of the variable , and , more DEVELOPMENT OF FUNCTIONS . 69.
... by particular methods . The preceding Theorems sometimes fail from the function which is to be expanded becoming infinite or indeterminate for particular values of the variable , and , more DEVELOPMENT OF FUNCTIONS . 69.
Сторінка 71
... preceding examples , we find for determining the coefficient of the general term , an + 1 = 1 n + 1 1.3 ' n - 2 2.4 a - 4 + & c . } . Also , it is easily seen , that a = 1 , therefore sin - 1 x = 1 + x + 2x3 + 5 x1 20a + 1.2 1.2.3 1.2 ...
... preceding examples , we find for determining the coefficient of the general term , an + 1 = 1 n + 1 1.3 ' n - 2 2.4 a - 4 + & c . } . Also , it is easily seen , that a = 1 , therefore sin - 1 x = 1 + x + 2x3 + 5 x1 20a + 1.2 1.2.3 1.2 ...
Сторінка 91
... preceding methods are applicable . Let x and y be func- tions of a and u = , then if for x = a x = 0 , y O we have u = 0o , = ≈ = ∞ , y = 0 we have u∞o , = 1 ± ∞ . x = 1 , y = we have u = Now since = € 1ogz , u = & log ; and these ...
... preceding methods are applicable . Let x and y be func- tions of a and u = , then if for x = a x = 0 , y O we have u = 0o , = ≈ = ∞ , y = 0 we have u∞o , = 1 ± ∞ . x = 1 , y = we have u = Now since = € 1ogz , u = & log ; and these ...
Сторінка 106
... preceding result , excepting that they shewed that the difference of 2 ' was due to an error in the calculations of Koenig - not to a mistake on the part of the bees . ( 33 ) To determine the greatest parabola which can be cut from a ...
... preceding result , excepting that they shewed that the difference of 2 ' was due to an error in the calculations of Koenig - not to a mistake on the part of the bees . ( 33 ) To determine the greatest parabola which can be cut from a ...
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