Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 56
Сторінка 46
... arbitrary function from the equation 2 = x хуф ( у ) . Differentiating with respect to a only , dz dz = у ф ( y ) ; and therefore a = 0 . dx dx ( 16 ) Eliminate the function from the equation - y - nz = p ( x − m≈ ) . Differentiating ...
... arbitrary function from the equation 2 = x хуф ( у ) . Differentiating with respect to a only , dz dz = у ф ( y ) ; and therefore a = 0 . dx dx ( 16 ) Eliminate the function from the equation - y - nz = p ( x − m≈ ) . Differentiating ...
Сторінка 47
... arbitrary functions are really equivalent to one only , for the original equation may be put under the form x2 x = a ^ { p ( i ) + ( i ) + ( i ) } - " r ( 2 ) = This is the reason why both functions disappear after one ELIMINATION OF ...
... arbitrary functions are really equivalent to one only , for the original equation may be put under the form x2 x = a ^ { p ( i ) + ( i ) + ( i ) } - " r ( 2 ) = This is the reason why both functions disappear after one ELIMINATION OF ...
Сторінка 49
... arbitrary their logarithms are also arbitrary functions , and we may replace them by the general characteristics F and f . Therefore , differentiating with respect to x and y successively , 1 dz z dx 1 dx - = bF ' ( ay + bx ) - bf ...
... arbitrary their logarithms are also arbitrary functions , and we may replace them by the general characteristics F and f . Therefore , differentiating with respect to x and y successively , 1 dz z dx 1 dx - = bF ' ( ay + bx ) - bf ...
Сторінка 50
... arbitrary functions from ( 1 ) x ƒ ( a ) + y $ ( a ) + ≈ † ( a ) = 1 , where a is a function of x , y , and ... arbitrary function from the equation 50 ELIMINATION OF CONSTANTS AND FUNCTIONS .
... arbitrary functions from ( 1 ) x ƒ ( a ) + y $ ( a ) + ≈ † ( a ) = 1 , where a is a function of x , y , and ... arbitrary function from the equation 50 ELIMINATION OF CONSTANTS AND FUNCTIONS .
Сторінка 51
Duncan Farquharson Gregory William Walton. ( 24 ) Eliminate the arbitrary function from the equation x y U = Since f Ꮖ y 2 " > v dimensions , we know that " y 2 X is a homogeneous function of m du du du 20 + y +8 dx dy dx ( 25 ) If u ...
Duncan Farquharson Gregory William Walton. ( 24 ) Eliminate the arbitrary function from the equation x y U = Since f Ꮖ y 2 " > v dimensions , we know that " y 2 X is a homogeneous function of m du du du 20 + y +8 dx dy dx ( 25 ) If u ...
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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