| Elias Loomis - 1879 - 398 páginas
...+ Oj2+, etc.=A'+B'x+C'x2 + , etc., must be satisfied for each and every value given to x, then Hte coefficients of the like powers of x in the two members are equal each to each. For, since this equation must be satisfied for every value of x, it must be satisfied when x=0. But... | |
| James Morford Taylor - 1889 - 400 páginas
...In the first member of (2), the coefficient of any power of x that does not appear is zero. Equating the coefficients of the like powers of x in the two members of (2), we obtain Solving the system of equations (3), we obtain ."0 'j «I — Ij ^2 1' s — ^' 4... | |
| Emerson Elbridge White - 1896 - 418 páginas
...CW + D'à? + ••• (1) is such that for every value of x the equation is an identity (§ 624), then the coefficients of the like powers of x in the two members are equal. For, since the equation is satisfied by any value of ж, let x = 0. Then every term containing x equals... | |
| William Anthony Granville, Percey Franklyn Smith - 1904 - 490 páginas
...+ 2)z + C(z - l)x = (A + B+ C)xt + (A +2.B- C)z- 2Л. Since this equation is an identity, we equate the coefficients of the like powers of x in the two members according to the method of Undetermined Coefficients, and obtain the three simultaneous equations (C)... | |
| William Guy Peck - 1870 - 244 páginas
...1) a2 + 1 a .+ 1 Clearing of fractions, and reducing, X = ^X^ + (Jt + 5)X + ^1 + (7x2 + (7 Equating the coefficients of the like powers of x in the two members, and solving the resulting equations, we haye, A=\, B=\, and 0 = -±. Substituting in (1), and multiplying... | |
| |