Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 20
Сторінка 22
... finite number of terms having positive indices , the terms in the product of ( 2 ) and ( 3 ) which contain negative indices must disappear of themselves . Hence taking the terms with positive indices only ( - ( e + 1 ) +1 . d u dxr ...
... finite number of terms having positive indices , the terms in the product of ( 2 ) and ( 3 ) which contain negative indices must disappear of themselves . Hence taking the terms with positive indices only ( - ( e + 1 ) +1 . d u dxr ...
Сторінка 52
... Finite Differences , and makes no application of it , or remark on its importance . The following is the statement of the theorem : If u = f ( r ) and receive an increment h , then f ( x + h ) = u + du d2 u h2 h + dx dx2 1.2 ď u h3 + ...
... Finite Differences , and makes no application of it , or remark on its importance . The following is the statement of the theorem : If u = f ( r ) and receive an increment h , then f ( x + h ) = u + du d2 u h2 h + dx dx2 1.2 ď u h3 + ...
Сторінка 152
... finite distance from the origin , is a tangent to the curve at an infinite distance , it appears that if x , or y , remain finite when a or y are infinite , their values will determine the position of the asymptote . A more convenient ...
... finite distance from the origin , is a tangent to the curve at an infinite distance , it appears that if x , or y , remain finite when a or y are infinite , their values will determine the position of the asymptote . A more convenient ...
Сторінка 153
... finite value of ≈ in the numerator can make f ( x ) = ∞ . These values of a being found , the ordi- nates drawn through them are asymptotes to the curve . ( 13 ) Let the equation to the curve be y3 = ax2 + x3 . Then dy 2ax + 3x2 di 3y ...
... finite value of ≈ in the numerator can make f ( x ) = ∞ . These values of a being found , the ordi- nates drawn through them are asymptotes to the curve . ( 13 ) Let the equation to the curve be y3 = ax2 + x3 . Then dy 2ax + 3x2 di 3y ...
Сторінка 155
... finite value for the intercepts of the tangents , then these determine the position of the asymptotes . ( 16 ) Let ay3 − bx3 + c2xy = 0 - be the equation to the curve : then assuming y = xx , we find c2x2 x = C2 % b - ax3 ' y = b - Now ...
... finite value for the intercepts of the tangents , then these determine the position of the asymptotes . ( 16 ) Let ay3 − bx3 + c2xy = 0 - be the equation to the curve : then assuming y = xx , we find c2x2 x = C2 % b - ax3 ' y = b - Now ...
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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