Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 100
Page 15
... becomes ( u + h + chủ ) ; ď u and will be the coefficient of h 1.2 ... in the expan- dx * sion of this trinomial . Developing it as a binomial , of which u + u'h is the first term , we obtain ( u + b ) + n ( u + h ) n - ch ° + n ( n 1 ) ...
... becomes ( u + h + chủ ) ; ď u and will be the coefficient of h 1.2 ... in the expan- dx * sion of this trinomial . Developing it as a binomial , of which u + u'h is the first term , we obtain ( u + b ) + n ( u + h ) n - ch ° + n ( n 1 ) ...
Page 19
... become x + h , u becomes © ( x + h ) 2 = C ( x2 + 2x h + h2 ) = = 6 © × 2 . 62 cxh ̧ ̧ch2 Now sh ( 2 cx ) 2 ( 2cx ) 3 = 1 + 2cx h + h2 + h3 + & c . 1.2 1.2.3 c2 C3 h1 + ho + & c . 1. 2 1.2.3 and ech2 = 1 + ch2 + Multiplying these ...
... become x + h , u becomes © ( x + h ) 2 = C ( x2 + 2x h + h2 ) = = 6 © × 2 . 62 cxh ̧ ̧ch2 Now sh ( 2 cx ) 2 ( 2cx ) 3 = 1 + 2cx h + h2 + h3 + & c . 1.2 1.2.3 c2 C3 h1 + ho + & c . 1. 2 1.2.3 and ech2 = 1 + ch2 + Multiplying these ...
Page 36
... becomes SS V ( dx dy dx dy - do dr dr de dr de . If we had three variables x , y , z to be transformed into three others p , q , r , we should have three equations of the form dx = Pdp + Qdq + Rdr , dy = 36 CHANGE OF THE INDEPENDENT ...
... becomes SS V ( dx dy dx dy - do dr dr de dr de . If we had three variables x , y , z to be transformed into three others p , q , r , we should have three equations of the form dx = Pdp + Qdq + Rdr , dy = 36 CHANGE OF THE INDEPENDENT ...
Page 40
... becomes ď2 ( rV ) 1 d2 V d dV 2 ° + sin2 0 dr2 sin 0 do d . cos 0 d.cos 。) = = 0 . This important equation is the basis of the Mathematical Theories of Attraction and Electricity . The artifice here used is given by Mr A. Smith in the ...
... becomes ď2 ( rV ) 1 d2 V d dV 2 ° + sin2 0 dr2 sin 0 do d . cos 0 d.cos 。) = = 0 . This important equation is the basis of the Mathematical Theories of Attraction and Electricity . The artifice here used is given by Mr A. Smith in the ...
Page 41
... for the volume of any solid referred to rectangular co - ordinates : and it becomes fffr2 dr sine de dp when referred to polar co - ordinates . ( 10 ) Having given a function of x and CHANGE OF THE INDEPENDENT VARIABLE . 41.
... for the volume of any solid referred to rectangular co - ordinates : and it becomes fffr2 dr sine de dp when referred to polar co - ordinates . ( 10 ) Having given a function of x and CHANGE OF THE INDEPENDENT VARIABLE . 41.
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