Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 57
Page 46
... arbitrary function from the equation ≈ = xyp ( y ) . Differentiating with respect to a only , dz dx = y ( y ) ; and therefore c ( 16 ) Eliminate the function dz = 0 . dx from the equation - y N≈ = - $ ( x − mx ) . Differentiating ...
... arbitrary function from the equation ≈ = xyp ( y ) . Differentiating with respect to a only , dz dx = y ( y ) ; and therefore c ( 16 ) Eliminate the function dz = 0 . dx from the equation - y N≈ = - $ ( x − mx ) . Differentiating ...
Page 47
... arbitrary functions are really equivalent to one only , for the original equation may be put under the form f · = ~ {。( 1 ) + ( - ) * × ( ) } = ~ ~ ( ? ) . x = xn 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 f · = ~ {。( 1 ) + ( - ) * × ( ) } = ~ ~ ( ? ) . x = xn This is the reason why both functions disappear after one ELIMINATION OF ...
Page 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 dx bF ' ( ay + bx ) – bƒ ' ( ay – bx ) , = z ...
... 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 dx bF ' ( ay + bx ) – bƒ ' ( ay – bx ) , = z ...
Page 50
... arbitrary functions from ( 1 ) xf ( a ) + yp ( a ) + ≈ √ ( a ) = 1 , where a is a function of a , y , and ≈ given by the equation ( 2 ) x f ' ( a ) + y p ' ( a ) + ≈ f ' ( a ) = 0 ; f ' , ' , being the differential coefficients of f ...
... arbitrary functions from ( 1 ) xf ( a ) + yp ( a ) + ≈ √ ( a ) = 1 , where a is a function of a , y , and ≈ given by the equation ( 2 ) x f ' ( a ) + y p ' ( a ) + ≈ f ' ( a ) = 0 ; f ' , ' , being the differential coefficients of f ...
Page 51
D. F. Gregory. ( 24 ) Eliminate the arbitrary function from the equation y X W = > , Since af y 8 , V dimensions , we know that ( 25 ) is a homogeneous function of m du du du 20 + y +2 dx dy dx If u = f ( x , y ) = F ( r , ≈ ) , = mu ...
D. F. Gregory. ( 24 ) Eliminate the arbitrary function from the equation y X W = > , Since af y 8 , V dimensions , we know that ( 25 ) is a homogeneous function of m du du du 20 + y +2 dx dy dx If u = f ( x , y ) = F ( r , ≈ ) , = mu ...
Other editions - View all
Common terms and phrases
a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx 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 radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³