Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 41
Сторінка 21
... 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 ( ε2 + 1 ) ' + 1 d'u dx ( r + 1 ) = ( − ) ' [ 1'e ' * — { 2r ...
... 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 ( ε2 + 1 ) ' + 1 d'u dx ( r + 1 ) = ( − ) ' [ 1'e ' * — { 2r ...
Сторінка 61
... series u = -- x3 - a2 a3 Taking the positive value of a , u = a - 00 2 - x5 a1 - & c . v2 3x3 + 8 a , & c . 16a2 Taking the negative value of a , x2 5.23 u = - a + 2 + + & c . 8 a Sa2 ( 13 ) If sin ya sin ( a + DEVELOPMENT OF FUNCTIONS .
... series u = -- x3 - a2 a3 Taking the positive value of a , u = a - 00 2 - x5 a1 - & c . v2 3x3 + 8 a , & c . 16a2 Taking the negative value of a , x2 5.23 u = - a + 2 + + & c . 8 a Sa2 ( 13 ) If sin ya sin ( a + DEVELOPMENT OF FUNCTIONS .
Сторінка 62
... positive integer . dy dy Differentiating , cos y = sin ( a + y ) + x cos ( a + y ) da dx putting = 0 , y = rπ , we have a sin ( a + rπ ) f ' ( 0 ) = COS ↑ π = sin a . Differentiating again , cos y day dx2 - sin y dx ' dy 2 dy = 2 cos ...
... positive integer . dy dy Differentiating , cos y = sin ( a + y ) + x cos ( a + y ) da dx putting = 0 , y = rπ , we have a sin ( a + rπ ) f ' ( 0 ) = COS ↑ π = sin a . Differentiating again , cos y day dx2 - sin y dx ' dy 2 dy = 2 cos ...
Сторінка 66
... c3 ( a b3b 3 + & c . } , the series only continuing so long as there are positive powers b of " a that is , negative powers of a or g . . Equations Numériques , p . 225 . ( 10 ) Let a - by + cy ' 66 DEVELOPMENT OF FUNCTIONS .
... c3 ( a b3b 3 + & c . } , the series only continuing so long as there are positive powers b of " a that is , negative powers of a or g . . Equations Numériques , p . 225 . ( 10 ) Let a - by + cy ' 66 DEVELOPMENT OF FUNCTIONS .
Сторінка 67
... positive powers of b a If in these equations we substitute find the sum of the inverse nt th for y , and then y powers of the roots of the transformed equation , we obtain a series for the direct th powers of the roots of the original ...
... positive powers of b a If in these equations we substitute find the sum of the inverse nt th for y , and then y powers of the roots of the transformed equation , we obtain a series for the direct th powers of the roots of the original ...
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy 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 plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³