Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 63
Сторінка 21
... preceding formula ď u dx + ( − ) 3 r ( r − 1 ) ( 2x ) TM -2 = c ( - ) * x2 { ( − ) ' 3 ( 2x ) ′ + ( − ) ' ï'r ( = + ( − ) ' ï2 r ( r − 1 ) ... ( r – 3 ) 1.2 Now generally ( - ) } = c ( − ) » 1⁄2 ‚ and 6 ( - ) * x2 ( − ) * p = cos ...
... preceding formula ď u dx + ( − ) 3 r ( r − 1 ) ( 2x ) TM -2 = c ( - ) * x2 { ( − ) ' 3 ( 2x ) ′ + ( − ) ' ï'r ( = + ( − ) ' ï2 r ( r − 1 ) ... ( r – 3 ) 1.2 Now generally ( - ) } = c ( − ) » 1⁄2 ‚ and 6 ( - ) * x2 ( − ) * p = cos ...
Сторінка 40
... preceding example + ď v d2 V d Ꮩ 1 d V 1 dv + dy dx2 d p2 2 p2 dp2 p dp In exactly the same way , the equations of condition being similar , we find d2 V d2 V dp2 + dx2 d2 V = + 1 ď2 V + dr.2 r2 do2 1 d V - r dr Also , as in the first ...
... preceding example + ď v d2 V d Ꮩ 1 d V 1 dv + dy dx2 d p2 2 p2 dp2 p dp In exactly the same way , the equations of condition being similar , we find d2 V d2 V dp2 + dx2 d2 V = + 1 ď2 V + dr.2 r2 do2 1 d V - r dr Also , as in the first ...
Сторінка 55
... preceding example let h = -x , then tan1 ( x + h ) = tan 1 0 = : 0 ; therefore tan ̄1 x = sin y . sin y.x + ( sin y ) 2 sin 2 y git 001 + ( sin y ) 3 sin 3 y + ( sin y ) 1 sin 4 y + & c . 3 4 π cos y Now tan- ' = therefore -1 - y , and ...
... preceding example let h = -x , then tan1 ( x + h ) = tan 1 0 = : 0 ; therefore tan ̄1 x = sin y . sin y.x + ( sin y ) 2 sin 2 y git 001 + ( sin y ) 3 sin 3 y + ( sin y ) 1 sin 4 y + & c . 3 4 π cos y Now tan- ' = therefore -1 - y , and ...
Сторінка 63
... preceding made by assuming the given equation in y to be d . y = F { x + x + ( y ) } . Then if u = f ( y ) , and if we put ƒF ( x ) = f1 ( * ) , and __ƒF ( x ) = fi ( ~ ) , and $ F ( x ) = $ 1 ( ~ ) , dx d x2 u = ƒ ( y ) = ƒ¡ ( ≈ ) + ...
... preceding made by assuming the given equation in y to be d . y = F { x + x + ( y ) } . Then if u = f ( y ) , and if we put ƒF ( x ) = f1 ( * ) , and __ƒF ( x ) = fi ( ~ ) , and $ F ( x ) = $ 1 ( ~ ) , dx d x2 u = ƒ ( y ) = ƒ¡ ( ≈ ) + ...
Сторінка 64
... b 1 , C a2c2 y = 1 + a + 2 log a 1 1.2 = x = = b . Then C3 + & c . 1.2.3 + 32 ( log a ) 2 a3b = or y 1 + ca " , + 32 ( log a ) 2 See Ex . 15 of the preceding Section . a3c3 + & c . 1.2.3 ( 4 ) Let y = a + x log 64 DEVELOPMENT OF FUNCTIONS .
... b 1 , C a2c2 y = 1 + a + 2 log a 1 1.2 = x = = b . Then C3 + & c . 1.2.3 + 32 ( log a ) 2 a3b = or y 1 + ca " , + 32 ( log a ) 2 See Ex . 15 of the preceding Section . a3c3 + & c . 1.2.3 ( 4 ) Let y = a + x log 64 DEVELOPMENT OF FUNCTIONS .
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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