Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
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Сторінка 22
... equal to the second side of ( 1 ) , and as this last consists of a finite number of terms having positive indices , the terms in the product of ( 2 ) and ( 3 ) which contain negative indices must disappear of themselves . Hence taking ...
... equal to the second side of ( 1 ) , and as this last consists of a finite number of terms having positive indices , the terms in the product of ( 2 ) and ( 3 ) which contain negative indices must disappear of themselves . Hence taking ...
Сторінка 71
... equal to 1 . Hence we find x02 3x1 sinx 8.25 = 1 + x + 1.2 1.2.3.4 1.2.3.4.5 3x6 1.2.3.4.5.6 + & c . ( 3 ) Let W = Esin - 1 du 1 Then @ sin − 1 and = dx ( 1 − x2 ) 3 ( 1 − ∞ 2 ) − 3 = 1 + ¦ x2 + Therefore , assuming a series as in ...
... equal to 1 . Hence we find x02 3x1 sinx 8.25 = 1 + x + 1.2 1.2.3.4 1.2.3.4.5 3x6 1.2.3.4.5.6 + & c . ( 3 ) Let W = Esin - 1 du 1 Then @ sin − 1 and = dx ( 1 − x2 ) 3 ( 1 − ∞ 2 ) − 3 = 1 + ¦ x2 + Therefore , assuming a series as in ...
Сторінка 77
... 1 multiplied by 22 ( - ) " . By what has preceded it appears , therefore , to be equal to 22n ( 2n - 1 ) 1.2 ... ( 2n ) B2n - 1 ' Hence , giving n successive values , we find tan DEVELOPMENT OF FUNCTIONS . 77 PART II.
... 1 multiplied by 22 ( - ) " . By what has preceded it appears , therefore , to be equal to 22n ( 2n - 1 ) 1.2 ... ( 2n ) B2n - 1 ' Hence , giving n successive values , we find tan DEVELOPMENT OF FUNCTIONS . 77 PART II.
Сторінка 78
... equal to 00 multiplied by ( - ) " 22 " : 1 ( - ) " 22 " B2n - 1 1.2.3 ... ( 2n ) Hence we have cot = 1 Ꮎ - 22 1.2 B10- ᏴᎾ 24 B303 - & c . 1.2.3.4 CHAPTER VI . EVALUATION OF FUNCTIONS WHICH FOR CERTAIN VALUES 78 DEVELOPMENT OF FUNCTIONS .
... equal to 00 multiplied by ( - ) " 22 " : 1 ( - ) " 22 " B2n - 1 1.2.3 ... ( 2n ) Hence we have cot = 1 Ꮎ - 22 1.2 B10- ᏴᎾ 24 B303 - & c . 1.2.3.4 CHAPTER VI . EVALUATION OF FUNCTIONS WHICH FOR CERTAIN VALUES 78 DEVELOPMENT OF FUNCTIONS .
Сторінка 79
... equal to a . There- fore we may say generally that the true value of u when x = a is u = P ( ) Q ( n ) 5 P ) and Q " being the first differential coefficients of P and Q which do not vanish simultaneously when x is put equal to a . This ...
... equal to a . There- fore we may say generally that the true value of u when x = a is u = P ( ) Q ( n ) 5 P ) and Q " being the first differential coefficients of P and Q which do not vanish simultaneously when x is put equal to a . This ...
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a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³