Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 92
Сторінка 19
... . r , we find d'u dx " = + - -2 { c ' ( 2x ) ' + r ( r − 1 ) c * - ' ( 2 x ) * −2 - r ( r − 1 ) ... ( r – 3 ) 1.2 - c ' − 2 ( 2x ) ' ~ ' + & c . } ( 26 ) From this we can determine the successive 2-2 SUCCESSIVE DIFFERENTIATION . 19.
... . r , we find d'u dx " = + - -2 { c ' ( 2x ) ' + r ( r − 1 ) c * - ' ( 2 x ) * −2 - r ( r − 1 ) ... ( r – 3 ) 1.2 - c ' − 2 ( 2x ) ' ~ ' + & c . } ( 26 ) From this we can determine the successive 2-2 SUCCESSIVE DIFFERENTIATION . 19.
Сторінка 20
Duncan Farquharson Gregory William Walton. ( 26 ) From this we can determine the successive dif- ferentials of cos 2 and sin x2 . Let u = cos x2 + ( − ) 1 sin a2 ( − ) sin x = g ( - ) * Then differentiating by the preceding formula ďu ...
Duncan Farquharson Gregory William Walton. ( 26 ) From this we can determine the successive dif- ferentials of cos 2 and sin x2 . Let u = cos x2 + ( − ) 1 sin a2 ( − ) sin x = g ( - ) * Then differentiating by the preceding formula ďu ...
Сторінка 37
... determine da by supposing dy = 0 , and dx = 0 , and then eliminating two of the three quantities dp , dq , dr . Supposing we eliminate the last two we have da Mdp , M being a function of p , q , r . From this it follows that when dx = 0 ...
... determine da by supposing dy = 0 , and dx = 0 , and then eliminating two of the three quantities dp , dq , dr . Supposing we eliminate the last two we have da Mdp , M being a function of p , q , r . From this it follows that when dx = 0 ...
Сторінка 42
... determined by the equation y ? སྨ ? + b ? = 1 , it is required to transform 2 [ fdx dy { 1 + ( da ) + ( da ) " } into a function of 0 and dx when x = a sin cos p , and consequently dy y = b sine sin o , ≈ = c cos 0 . In this case dx dx ...
... determined by the equation y ? སྨ ? + b ? = 1 , it is required to transform 2 [ fdx dy { 1 + ( da ) + ( da ) " } into a function of 0 and dx when x = a sin cos p , and consequently dy y = b sine sin o , ≈ = c cos 0 . In this case dx dx ...
Сторінка 70
... determining the successive differential coefficients . Recourse must then be had to particular ar- tifices depending on the nature of the function which is given . One of the most useful methods is to assume a series with indeterminate ...
... determining the successive differential coefficients . Recourse must then be had to particular ar- tifices depending on the nature of the function which is given . One of the most useful methods is to assume a series with indeterminate ...
Зміст
1 | |
9 | |
28 | |
43 | |
52 | |
77 | |
79 | |
94 | |
224 | |
237 | |
249 | |
271 | |
282 | |
291 | |
340 | |
351 | |
129 | |
132 | |
144 | |
162 | |
175 | |
188 | |
200 | |
386 | |
400 | |
412 | |
440 | |
464 | |
506 | |
Інші видання - Показати все
Загальні терміни та фрази
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