Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 95
Сторінка 20
... , we find d u dx " = + { c ' ( 2x ) ' + r ( r − 1 ) cr − 1 ( 2x ) ′′ - 2 r ( r− 1 ) ... ( r − 3 ) 1.2 - cr - 2 ( 2x ) ” − 1 + & c . } ( 26 ) From this we can determine the successive 20 SUCCESSIVE DIFFERENTIATION .
... , we find d u dx " = + { c ' ( 2x ) ' + r ( r − 1 ) cr − 1 ( 2x ) ′′ - 2 r ( r− 1 ) ... ( r − 3 ) 1.2 - cr - 2 ( 2x ) ” − 1 + & c . } ( 26 ) From this we can determine the successive 20 SUCCESSIVE DIFFERENTIATION .
Сторінка 21
Duncan Farquharson Gregory. ( 26 ) From this we can determine the successive dif- ferentials of cos.r2 and sin x2 . Let u = cos x2 + ( − ) 3 sin æ2 ( − ) $ x2 . = E Then differentiating by the preceding formula ď u dx + ( − ) 3 r ( r ...
Duncan Farquharson Gregory. ( 26 ) From this we can determine the successive dif- ferentials of cos.r2 and sin x2 . Let u = cos x2 + ( − ) 3 sin æ2 ( − ) $ x2 . = E Then differentiating by the preceding formula ď u dx + ( − ) 3 r ( r ...
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 dx = Mdp , From this it follows that M being a function of p , q , r . when do 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 dx = Mdp , From this it follows that M being a function of p , q , r . when do 0 ...
Сторінка 41
... the volume of any solid referred to rectangular co - ordinates : and it becomes fffr2 dr sine de dp when referred to polar co - ordinates . y determined ( 10 ) Having given a function of CHANGE OF THE INDEPENDENT VARIABLE . 41.
... the volume of any solid referred to rectangular co - ordinates : and it becomes fffr2 dr sine de dp when referred to polar co - ordinates . y determined ( 10 ) Having given a function of CHANGE OF THE INDEPENDENT VARIABLE . 41.
Сторінка 42
Duncan Farquharson Gregory. y determined ( 10 ) Having given a function of a and by the equation Ta شرح 2 + + = 1 , a2 b2 it is required to transform 2 [ [ dwdy { 1 + ( da ) ' + ( d * ) * } * dy { 1 into a function of 0 and when x = a ...
Duncan Farquharson Gregory. y determined ( 10 ) Having given a function of a and by the equation Ta شرح 2 + + = 1 , a2 b2 it is required to transform 2 [ [ dwdy { 1 + ( da ) ' + ( d * ) * } * dy { 1 into a function of 0 and when x = a ...
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Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³