Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Результати 6-10 із 68
Сторінка 43
D. F. Gregory. CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS OF DIFFERENTIATION . Ex . ( 1 ) y2 = ax + b ......... ( 1 ) . To eliminate b , differentiate , when we have dy 2y a ......... ( 2 ) . dx To eliminate a ...
D. F. Gregory. CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS OF DIFFERENTIATION . Ex . ( 1 ) y2 = ax + b ......... ( 1 ) . To eliminate b , differentiate , when we have dy 2y a ......... ( 2 ) . dx To eliminate a ...
Сторінка 58
... means of this series that Newton calculated the Commercium Epistolicum , p . 85 , 2nd Edit . value of π . ( 5 ) Let utan1 ( ) . By means of Chap . 11. Sec . 1 , Ex . 24 , we find tan1⁄4x = x - + 3 This is Gregorie's series . p . 98 ...
... means of this series that Newton calculated the Commercium Epistolicum , p . 85 , 2nd Edit . value of π . ( 5 ) Let utan1 ( ) . By means of Chap . 11. Sec . 1 , Ex . 24 , we find tan1⁄4x = x - + 3 This is Gregorie's series . p . 98 ...
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... means of the double sign . ( 11 ) Let u3 - 6ux - When x = = 0 , 8 = 0 . u3 = 8 , u = = ( 8 ) . The possible root of this is 2 , and if we take it , we find by the same method as in the last example the series 1 X03 4 u = 2 + x - + 2 1.2 ...
... means of the double sign . ( 11 ) Let u3 - 6ux - When x = = 0 , 8 = 0 . u3 = 8 , u = = ( 8 ) . The possible root of this is 2 , and if we take it , we find by the same method as in the last example the series 1 X03 4 u = 2 + x - + 2 1.2 ...
Сторінка 63
... means of expanding implicit functions , is to be found in the Theorems of Lagrange and Laplace , to which we now proceed . SECT . 3. Theorems of Lagrange and Laplace . If y be given in an equation of the form y = x + xp ( y ) , and if u ...
... means of expanding implicit functions , is to be found in the Theorems of Lagrange and Laplace , to which we now proceed . SECT . 3. Theorems of Lagrange and Laplace . If y be given in an equation of the form y = x + xp ( y ) , and if u ...
Сторінка 70
... c . } . 1 2 1 2 N Comparing now the coefficients of a " in ( 1 ) and ( 5 ) we find 1 an + 1 = n + 1 an - 2 an - 3 do + + & c . + 1.2 1.2.3 1.2 n whence any coefficient is determined by means of those which 70 DEVELOPMENT OF FUNCTIONS .
... c . } . 1 2 1 2 N Comparing now the coefficients of a " in ( 1 ) and ( 5 ) we find 1 an + 1 = n + 1 an - 2 an - 3 do + + & c . + 1.2 1.2.3 1.2 n whence any coefficient is determined by means of those which 70 DEVELOPMENT OF FUNCTIONS .
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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