Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 43
Сторінка iii
... similar plan , but with such modifications as seemed called for by the increased cultivation of Analysis in this University . Accordingly I have not limited myself to the mere collection of Examples and Problems illustrative of Theorems ...
... similar plan , but with such modifications as seemed called for by the increased cultivation of Analysis in this University . Accordingly I have not limited myself to the mere collection of Examples and Problems illustrative of Theorems ...
Сторінка 40
... similar , we find dev d2 V + = d'V 1 + d2 V + d p2 do dx2 dr r2 1 dv - r dr Also , as in the first part of the last example , 1 dv 1 dv = p dp r dr cot 0 dv + do Adding these three expressions , d'V d'V de V + + dy d dx d2 V 1 d'V 1 d2 ...
... similar , we find dev d2 V + = d'V 1 + d2 V + d p2 do dx2 dr r2 1 dv - r dr Also , as in the first part of the last example , 1 dv 1 dv = p dp r dr cot 0 dv + do Adding these three expressions , d'V d'V de V + + dy d dx d2 V 1 d'V 1 d2 ...
Сторінка 62
... similar manner we should find ƒ " " ( 0 ) = 2 sin a 3 - 4 ( sin a ) " } , and so on ; therefore , substituting in Maclaurin's Theorem , X y = rπ + sin a + sin 2 a 1 1.2 +2 sin a { 3-4 ( sin a ) " } x3 1.2.3 + & c . ( 14 ) If u " log u ...
... similar manner we should find ƒ " " ( 0 ) = 2 sin a 3 - 4 ( sin a ) " } , and so on ; therefore , substituting in Maclaurin's Theorem , X y = rπ + sin a + sin 2 a 1 1.2 +2 sin a { 3-4 ( sin a ) " } x3 1.2.3 + & c . ( 14 ) If u " log u ...
Сторінка 90
... similar kind relating to the summation of series in Euler's Cale . Diff p . 760 , seq . Sometimes the value of an indeterminate function may be most readily found by throwing it into a form in which its real nature is more easily scen ...
... similar kind relating to the summation of series in Euler's Cale . Diff p . 760 , seq . Sometimes the value of an indeterminate function may be most readily found by throwing it into a form in which its real nature is more easily scen ...
Сторінка 92
... . ( 15 ) u = ( cot a ) sin a 0 = when a = 0 . By similar considerations it appears that ( 46 ) 21 = ( cot a ) sin r - 1 when a = 0 . ( 1 + na ) ' when a = 0 . log ( 1+ nx ) Here u = € log 92 EVALUATION OF INDETERMINATE FUNCTIONS .
... . ( 15 ) u = ( cot a ) sin a 0 = when a = 0 . By similar considerations it appears that ( 46 ) 21 = ( cot a ) sin r - 1 when a = 0 . ( 1 + na ) ' when a = 0 . log ( 1+ nx ) Here u = € log 92 EVALUATION OF INDETERMINATE FUNCTIONS .
Інші видання - Показати все
Загальні терміни та фрази
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