A Treatise on Infinitesimal Calculus ... |
From inside the book
Results 6-10 of 20
Page 143
... approximate value of the product of n numbers integral or fractional , in arithmetical pro- gression , of which the common difference is unity . If m = 1 , 1.2.3 ... n = ( 1 + n ) " + } e ̃ " . ( 207 ) Now the difference between the ...
... approximate value of the product of n numbers integral or fractional , in arithmetical pro- gression , of which the common difference is unity . If m = 1 , 1.2.3 ... n = ( 1 + n ) " + } e ̃ " . ( 207 ) Now the difference between the ...
Page 144
... approximate value for the product of the factorials , but we shall hereafter be able to correct it for the particular case given in ( 208 ) , viz . when n = ∞ . Again , if ( 205 ) is applied to the Example in Art . 112 , and the range ...
... approximate value for the product of the factorials , but we shall hereafter be able to correct it for the particular case given in ( 208 ) , viz . when n = ∞ . Again , if ( 205 ) is applied to the Example in Art . 112 , and the range ...
Page 145
... F ( XO ) = Ayo = Yi - Yoj △ 2F ( x ) = A1 - Ayo = Y2 - 2Y1 + Yoi △ 3F ( x ) = Y3-3y2 + 3y1 — Yo ; ( 20 ) PRICE , VOL . II . ( 214 ) so that from a geometrical point of view yo , 114. ] 145 METHODS OF APPROXIMATION .
... F ( XO ) = Ayo = Yi - Yoj △ 2F ( x ) = A1 - Ayo = Y2 - 2Y1 + Yoi △ 3F ( x ) = Y3-3y2 + 3y1 — Yo ; ( 20 ) PRICE , VOL . II . ( 214 ) so that from a geometrical point of view yo , 114. ] 145 METHODS OF APPROXIMATION .
Page 146
... approximation can be successfully applied , it is necessary that the values of these differences should rapidly ... approximate values to the definite integral . Thus , if we omit all terms after A2F ( x ) , we have dx n2 n3 n2 2 ...
... approximation can be successfully applied , it is necessary that the values of these differences should rapidly ... approximate values to the definite integral . Thus , if we omit all terms after A2F ( x ) , we have dx n2 n3 n2 2 ...
Page 147
... approximate value of the dx definite integral ( * % ( 1 - x3 ) ? : since for all values of x included within the range of integration , 1 1 > > 1 ; ( 1 − x2 ) 3 ... APPROXIMATION . Approximate values given by the forms of definite integrals.
... approximate value of the dx definite integral ( * % ( 1 - x3 ) ? : since for all values of x included within the range of integration , 1 1 > > 1 ; ( 1 − x2 ) 3 ... APPROXIMATION . Approximate values given by the forms of definite integrals.
Contents
1 | |
4 | |
18 | |
41 | |
48 | |
53 | |
71 | |
83 | |
322 | |
323 | |
324 | |
326 | |
327 | |
328 | |
330 | |
332 | |
85 | |
98 | |
104 | |
105 | |
108 | |
111 | |
117 | |
121 | |
123 | |
130 | |
134 | |
144 | |
150 | |
154 | |
155 | |
161 | |
169 | |
177 | |
184 | |
190 | |
197 | |
206 | |
210 | |
217 | |
222 | |
224 | |
231 | |
240 | |
249 | |
255 | |
256 | |
267 | |
279 | |
283 | |
287 | |
290 | |
302 | |
307 | |
308 | |
310 | |
311 | |
312 | |
313 | |
315 | |
316 | |
317 | |
319 | |
321 | |
333 | |
335 | |
337 | |
338 | |
339 | |
354 | |
366 | |
372 | |
376 | |
382 | |
388 | |
389 | |
395 | |
396 | |
403 | |
405 | |
411 | |
414 | |
420 | |
426 | |
427 | |
430 | |
436 | |
461 | |
482 | |
491 | |
511 | |
513 | |
520 | |
528 | |
556 | |
569 | |
589 | |
597 | |
606 | |
614 | |
615 | |
622 | |
629 | |
643 | |
651 | |
663 | |
666 | |
673 | |
680 | |
687 | |
693 | |
Other editions - View all
A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα