Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 64
Сторінка 15
... obtain ( u + b ) + n ( u + h ) n - ch ° + n ( n 1 ) ( u + u'h ) " - 2 c2h ++ & c . 1.2 Again , developing each binomial and taking only the terms which multiply h ' , we find that the term in ... 1.2 ( u + u'h ) " is n ( n - 1 ) ( n in ...
... obtain ( u + b ) + n ( u + h ) n - ch ° + n ( n 1 ) ( u + u'h ) " - 2 c2h ++ & c . 1.2 Again , developing each binomial and taking only the terms which multiply h ' , we find that the term in ... 1.2 ( u + u'h ) " is n ( n - 1 ) ( n in ...
Сторінка 16
D. F. Gregory. By developing in a different manner a more convenient formula may be obtained : ( n + h + ch ) " = " ( 1 + = u ' u " { ( 1 + h ) 2 + 2u 4ис - u ' h + h2 ) " u ገ 4u2 и But 4uc u'2 = 4ac - b2 = e2 suppose . - Developing u ...
D. F. Gregory. By developing in a different manner a more convenient formula may be obtained : ( n + h + ch ) " = " ( 1 + = u ' u " { ( 1 + h ) 2 + 2u 4ис - u ' h + h2 ) " u ገ 4u2 и But 4uc u'2 = 4ac - b2 = e2 suppose . - Developing u ...
Сторінка 50
... obtain as the result of the elimination of the functions a2 - da 1 ( d ) " } - b2 Jd2 ≈ \ dy 2 2 - 2 dz = 0 . y ( 23 ) Eliminate the arbitrary functions from ( 1 ) xf ( a ) + yp ( a ) + ≈ √ ( a ) = 1 , where a is a function of a , y ...
... obtain as the result of the elimination of the functions a2 - da 1 ( d ) " } - b2 Jd2 ≈ \ dy 2 2 - 2 dz = 0 . y ( 23 ) Eliminate the arbitrary functions from ( 1 ) xf ( a ) + yp ( a ) + ≈ √ ( a ) = 1 , where a is a function of a , y ...
Сторінка 67
... obtain a series for the direct th powers of the roots of the original equation . ( 11 ) If we thus transform the equation in Ex . 10 , it becomes c - by + ay2 = 0 ; and if a , ẞ be the same quantities as before , ca n ( n = 3 ) c2 a2 a2 ...
... obtain a series for the direct th powers of the roots of the original equation . ( 11 ) If we thus transform the equation in Ex . 10 , it becomes c - by + ay2 = 0 ; and if a , ẞ be the same quantities as before , ca n ( n = 3 ) c2 a2 a2 ...
Сторінка 73
... Every term on the second side vanishes except the first , and there remains a = cos n ( 2r + 1 ) — · To find a1 , make x = ( 2r + 1 ) — in the second equation , when we obtain 2 π sin n ( 2 + 1 ) 2 π DEVELOPMENT OF FUNCTIONS . 73.
... Every term on the second side vanishes except the first , and there remains a = cos n ( 2r + 1 ) — · To find a1 , make x = ( 2r + 1 ) — in the second equation , when we obtain 2 π sin n ( 2 + 1 ) 2 π DEVELOPMENT OF FUNCTIONS . 73.
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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