Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 36
Сторінка 94
... maximum or minimum . " Equate to zero or dx infinity let a be a possible value of a obtained from either du dx of these equations ; then , if changes sign from + to or - - from to when , h being an indefinitely small quantity , a - h ...
... maximum or minimum . " Equate to zero or dx infinity let a be a possible value of a obtained from either du dx of these equations ; then , if changes sign from + to or - - from to when , h being an indefinitely small quantity , a - h ...
Сторінка 95
... maximum or a minimum accordingly as this differential coefficient is negative or positive . " If du dx = † ( x ) .v , † ( x ) being an es- sentially positive function of a , the following modification of this principle in many cases ...
... maximum or a minimum accordingly as this differential coefficient is negative or positive . " If du dx = † ( x ) .v , † ( x ) being an es- sentially positive function of a , the following modification of this principle in many cases ...
Сторінка 96
... maximum . 2n If u be a positive maximum or minimum , au2 " is also a maximum or minimum . If u be a negative maximum or minimum , au2 " will be a minimum or maximum . The same remarks apply to fractional powers of the function u ...
... maximum . 2n If u be a positive maximum or minimum , au2 " is also a maximum or minimum . If u be a negative maximum or minimum , au2 " will be a minimum or maximum . The same remarks apply to fractional powers of the function u ...
Сторінка 97
... maximum nor a minimum ; ) ( 4 ) the root 1 makes u a maximum ; the root 3 makes u a minimum . W = ( x − a ) " . - du = n ( x − a ) " - 1 ; - dx nor a minimum when n is odd , because x = a makes u = 0 , which is a minimum when n is ...
... maximum nor a minimum ; ) ( 4 ) the root 1 makes u a maximum ; the root 3 makes u a minimum . W = ( x − a ) " . - du = n ( x − a ) " - 1 ; - dx nor a minimum when n is odd , because x = a makes u = 0 , which is a minimum when n is ...
Сторінка 98
... maximum . This is the solution of the problem . To divide the number a into two parts , such that the product of the mth power of the one by the nth power of the other shall be a maximum . 20 du ( 6 ) u = - 1 + x2 da 1 - x2 ( 1 + x2 ) 2 ...
... maximum . This is the solution of the problem . To divide the number a into two parts , such that the product of the mth power of the one by the nth power of the other shall be a maximum . 20 du ( 6 ) u = - 1 + x2 da 1 - x2 ( 1 + x2 ) 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