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 17
... gives it under a form which is more convenient in practice ; 1 2 1 1 1 a2 + x2 ̄ ̄2a ( - ) ) { x + ( - ) -- ( - ) } ) } 2a ( - ) x + a a ( − ) $ Differentiating r times , d ( a ) = ( − ) r + 1 ̧ ~ ( ~ − 1 ) ... 2 . 1 { T • 1 a2 + x2 ...
... gives it under a form which is more convenient in practice ; 1 2 1 1 1 a2 + x2 ̄ ̄2a ( - ) ) { x + ( - ) -- ( - ) } ) } 2a ( - ) x + a a ( − ) $ Differentiating r times , d ( a ) = ( − ) r + 1 ̧ ~ ( ~ − 1 ) ... 2 . 1 { T • 1 a2 + x2 ...
Сторінка 29
... gives us the means of simplification . ( 1 ) Change the formula + ( y - a ) d2y -- = 0 dx2 + { . ( ) ++ into one where y is the independent variable . The result is 1 + dx dy 2 ď x - · ( y - - a ) = 0 . dy ' J ( 2 ) The expression for ...
... gives us the means of simplification . ( 1 ) Change the formula + ( y - a ) d2y -- = 0 dx2 + { . ( ) ++ into one where y is the independent variable . The result is 1 + dx dy 2 ď x - · ( y - - a ) = 0 . dy ' J ( 2 ) The expression for ...
Сторінка 37
... give it here , as the consideration of the particular conditions of any given transformation will usually give us its value more readily than a substitution in the general formula . * d R ( 1 ) Transform a d R y " dy dx having given x ...
... give it here , as the consideration of the particular conditions of any given transformation will usually give us its value more readily than a substitution in the general formula . * d R ( 1 ) Transform a d R y " dy dx having given x ...
Сторінка 61
... gives u = 0 , u = ± a . Taking the first of these values , we find the 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 ...
... gives u = 0 , u = ± a . Taking the first of these values , we find the 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 ...
Сторінка 65
... gives the least root of the equation . ( 6 ) Let y3 - ay + b yay + b = 0 : expand y " in terms of = a Here ƒ ( * ) = * " , P ( x ) = x3 , Whence 72 br y " = = = { 1 + n + a2 a a + b2 1 n ( n + 5 ) b1 1 1.2 a1 a2 + ♢ a n ( n + 7 ) ( n + ...
... gives the least root of the equation . ( 6 ) Let y3 - ay + b yay + b = 0 : expand y " in terms of = a Here ƒ ( * ) = * " , P ( x ) = x3 , Whence 72 br y " = = = { 1 + n + a2 a a + b2 1 n ( n + 5 ) b1 1 1.2 a1 a2 + ♢ a n ( n + 7 ) ( n + ...
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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