Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Сторінка 21
... easily seen on effecting two or three differentiations that the form d'u of dx must be z a‚é TM 3 + α , -16 ( r − 1 ) = + ɑ‚_2 € ( r − 2 ) ≈ + & c . + α1e * A ‚ z ( ε * + 1 ) ' + 1 Hence multiplying by ( e2 + 1 ) ' + 1 we must have ɑ ...
... easily seen on effecting two or three differentiations that the form d'u of dx must be z a‚é TM 3 + α , -16 ( r − 1 ) = + ɑ‚_2 € ( r − 2 ) ≈ + & c . + α1e * A ‚ z ( ε * + 1 ) ' + 1 Hence multiplying by ( e2 + 1 ) ' + 1 we must have ɑ ...
Сторінка 56
... easily found from the expression for tan1 ( x + h ) . For since du π cot x = - tan ̄x , 1 dx 1 and we have merely to substitute cot1 1 + a22 for tan - 1a and to change the signs of the terms beginning with the second : and as in this ...
... easily found from the expression for tan1 ( x + h ) . For since du π cot x = - tan ̄x , 1 dx 1 and we have merely to substitute cot1 1 + a22 for tan - 1a and to change the signs of the terms beginning with the second : and as in this ...
Сторінка 68
... easily seen that the series is the development of some function of a + h , which when h = 0 becomes u . Let u = f ( x ) , then f ( x + h ) = 0 . But since u = f ( x ) , x = f ( u ) , and if we call k the increment of u due to the ...
... easily seen that the series is the development of some function of a + h , which when h = 0 becomes u . Let u = f ( x ) , then f ( x + h ) = 0 . But since u = f ( x ) , x = f ( u ) , and if we call k the increment of u due to the ...
Сторінка 71
... easily found by putting a = 0 in the original equation , in which case a = € . Therefore , forming the successive coefficients from this first one , = ୧୧୦ 2x2 5203 + 151 + 52x5 1.2 1.2.3 1.2.3 . 4 1.2.3.4 . 5 € ̃ ̃ = € { 1 + ~ + + ...
... easily found by putting a = 0 in the original equation , in which case a = € . Therefore , forming the successive coefficients from this first one , = ୧୧୦ 2x2 5203 + 151 + 52x5 1.2 1.2.3 1.2.3 . 4 1.2.3.4 . 5 € ̃ ̃ = € { 1 + ~ + + ...
Сторінка 85
... easily seen that this includes the ordinary method of differentiation . ( 26 ) u = - ( x2 - a2 ) } ( x − a ) } when a = a . и - Let x = a + h , then ( 2 ah + h2 ) * ht h \ ( 2a ) h ( 1 + 2 a ᏂᎦ and expanding the binomial , ( 2a ) 1h1 ...
... easily seen that this includes the ordinary method of differentiation . ( 26 ) u = - ( x2 - a2 ) } ( x − a ) } when a = a . и - Let x = a + h , then ( 2 ah + h2 ) * ht h \ ( 2a ) h ( 1 + 2 a ᏂᎦ and expanding the binomial , ( 2a ) 1h1 ...
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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