Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 18
... function we should find d u = x a2 + x2 ? T X cos ( r + 1 ) 8 = ( - ) ' r ( r− 1 ) ... 2.1 a2 + x22 ( a2 + x ) ... functions are reduced to the required forms by differentiation in the same way as in Ex . 11 . x du u = ( 22 ) Let ( 1 ) d ...
... function we should find d u = x a2 + x2 ? T X cos ( r + 1 ) 8 = ( - ) ' r ( r− 1 ) ... 2.1 a2 + x22 ( a2 + x ) ... functions are reduced to the required forms by differentiation in the same way as in Ex . 11 . x du u = ( 22 ) Let ( 1 ) d ...
Сторінка 22
D. F. Gregory. SECT . 2 . Functions of Two or more Variables . If u be a function of two variables x and y , Ex . ( 1 ) dr + s u dy'dx drs u = dx'dy s = 1 , u = xy " ; r = 1 , du dx mxm - 1y " ; = d2 u dy da = m n xm m - 1 1y " - 1 du dy ...
D. F. Gregory. SECT . 2 . Functions of Two or more Variables . If u be a function of two variables x and y , Ex . ( 1 ) dr + s u dy'dx drs u = dx'dy s = 1 , u = xy " ; r = 1 , du dx mxm - 1y " ; = d2 u dy da = m n xm m - 1 1y " - 1 du dy ...
Сторінка 25
... functions of any number of variables , which from the frequent applications made of it ought to be noticed in this place . If u be a homogeneous algebraic function of n dimensions SUCCESSIVE DIFFERENTIATION . 25.
... functions of any number of variables , which from the frequent applications made of it ought to be noticed in this place . If u be a homogeneous algebraic function of n dimensions SUCCESSIVE DIFFERENTIATION . 25.
Сторінка 26
... function the degree of each term would be different , and the function when expanded not homogeneous . x ( 19 ) Let u = y3 + x3 y -x Then n = 2 and 2 ( y3 + x3 ) - du x- dx du + y dy ( 20 ) u = du dx + y du dy = 2y1 - 2y3 x + 2y x3 − 2 ...
... function the degree of each term would be different , and the function when expanded not homogeneous . x ( 19 ) Let u = y3 + x3 y -x Then n = 2 and 2 ( y3 + x3 ) - du x- dx du + y dy ( 20 ) u = du dx + y du dy = 2y1 - 2y3 x + 2y x3 − 2 ...
Сторінка 33
... function where s is the independent variable , having given that ds ( da ) 2 2 = 1 + ; dx ď3y dx d2x dy the result is - ds2 ds ds2 ds ( 12 ) Transform p dy 00 y dx ly + dx into a function of r and 0 , having given x = r cos 0 , y = r ...
... function where s is the independent variable , having given that ds ( da ) 2 2 = 1 + ; dx ď3y dx d2x dy the result is - ds2 ds ds2 ds ( 12 ) Transform p dy 00 y dx ly + dx into a function of r and 0 , having given x = r cos 0 , y = r ...
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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