Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Результати 1-5 із 67
Сторінка iii
... the principles of the Calculus . I wished by these means to render this Collection , as it were , complementary to those works , and , with the view of allowing it to be a read in connection with any of them , I have.
... the principles of the Calculus . I wished by these means to render this Collection , as it were , complementary to those works , and , with the view of allowing it to be a read in connection with any of them , I have.
Сторінка 1
... means of the theorem du du dy = dx dy dx y being some function of x , and u some function of y . This theorem may be extended to any number of functions , so that du du dv dz dy = do dv dx dy dx Ex . ( 1 ) Let u = Then y = a + bx ...
... means of the theorem du du dy = dx dy dx y being some function of x , and u some function of y . This theorem may be extended to any number of functions , so that du du dv dz dy = do dv dx dy dx Ex . ( 1 ) Let u = Then y = a + bx ...
Сторінка 28
... means of the formulæ , dy da d2 a dy dy2 = dx dx2 dx 3 dy dy d2 2 dy dx3 3 - dx dx dy dy dy3 5 dx dy and similarly for higher orders . The reader will find the demonstration of a general formula for the change of the nth differential ...
... means of the formulæ , dy da d2 a dy dy2 = dx dx2 dx 3 dy dy d2 2 dy dx3 3 - dx dx dy dy dy3 5 dx dy and similarly for higher orders . The reader will find the demonstration of a general formula for the change of the nth differential ...
Сторінка 42
... + ( da ) 2 + ( da ) * } * = ƒƒd0 dp sin 0 { a2b2 ( cos 0 ) 2 + ( c sin 0 ) 2 ( a2 sin2 p + b2 cos3p ) } 1 . Ivory , Phil . Trans . 1809 . CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS 42 CHANGE OF THE INDEPENDENT VARIABLE .
... + ( da ) 2 + ( da ) * } * = ƒƒd0 dp sin 0 { a2b2 ( cos 0 ) 2 + ( c sin 0 ) 2 ( a2 sin2 p + b2 cos3p ) } 1 . Ivory , Phil . Trans . 1809 . CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS 42 CHANGE OF THE INDEPENDENT VARIABLE .
Сторінка 43
Duncan Farquharson Gregory William Walton. CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS OF DIFFERENTIATION . J Ex . ( 1 ) y2 = = ax + b ......... ( 1 ) . To eliminate b , differentiate , when we have dy 2y a ......... ( 2 ) ...
Duncan Farquharson Gregory William Walton. CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS OF DIFFERENTIATION . J Ex . ( 1 ) y2 = = ax + b ......... ( 1 ) . To eliminate b , differentiate , when we have dy 2y a ......... ( 2 ) ...
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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