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 66
Сторінка v
... corresponding one for differentials , it is not applicable to all cases . Of this any one may satisfy himself by attempting to use it in transforming a multiple Integral from one system of independent variables to another , a problem ...
... corresponding one for differentials , it is not applicable to all cases . Of this any one may satisfy himself by attempting to use it in transforming a multiple Integral from one system of independent variables to another , a problem ...
Сторінка 52
... corresponding theorem in Finite Differences , and makes no application of it , or remark on its importance . The following is the statement of the theorem : If u = f ( x ) and a receive an increment h , then f ( x + h ) = u + du d2 u h2 ...
... corresponding theorem in Finite Differences , and makes no application of it , or remark on its importance . The following is the statement of the theorem : If u = f ( x ) and a receive an increment h , then f ( x + h ) = u + du d2 u h2 ...
Сторінка 76
... * 1 and consequently the corresponding 1 B2n - 1 is ( - ) " + 1 2n - 1 22n 1.2.3 ... ( 2n ) 1 x If therefore Can be the coefficient of a * " in > we have +1 the equation 2n - 1 ( - = C2n . 22 1.2.3 76 DEVELOPMENT OF FUNCTIONS .
... * 1 and consequently the corresponding 1 B2n - 1 is ( - ) " + 1 2n - 1 22n 1.2.3 ... ( 2n ) 1 x If therefore Can be the coefficient of a * " in > we have +1 the equation 2n - 1 ( - = C2n . 22 1.2.3 76 DEVELOPMENT OF FUNCTIONS .
Сторінка 94
... correspond respectively to a maximum or minimum value of u if no such change of sign takes place the value a of a must be rejected . By applying this process to each of the : roots of the equations du = 0 and dx du dx = 8 , we shall ...
... correspond respectively to a maximum or minimum value of u if no such change of sign takes place the value a of a must be rejected . By applying this process to each of the : roots of the equations du = 0 and dx du dx = 8 , we shall ...
Сторінка 103
... corresponding segment may be a maximum . Let a be the half - length of the arc , w the radius of the a circle ; then is the half - angle of the segment . - If u be the segment , u = ax - x2 sin Whence COS a 818 a 818 a COS is a maximum ...
... corresponding segment may be a maximum . Let a be the half - length of the arc , w the radius of the a circle ; then is the half - angle of the segment . - If u be the segment , u = ax - x2 sin Whence COS a 818 a 818 a COS is a maximum ...
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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