Elementary AlgebraMacmillan and Company, 1895 - 478 páginas |
Dentro del libro
Resultados 1-5 de 16
Página ix
... Expansion of Multinomials 313 316 319 319 321 Application when Index is Negative or Frac- tional 322 XL . Logarithms ... Expansion of Fractions into Series 360 Expansion of Surds into Series . 361 Reversion of Series . Partial Fractions ...
... Expansion of Multinomials 313 316 319 319 321 Application when Index is Negative or Frac- tional 322 XL . Logarithms ... Expansion of Fractions into Series 360 Expansion of Surds into Series . 361 Reversion of Series . Partial Fractions ...
Página 314
... expansion of ( x + a ) " when n is a positive integer . Consider the expression ( x + α ) ( x + b ) ( x + c ) ...... ( x + k ) , the number of factors being n . The expansion of this expression is the continued product of the n factors ...
... expansion of ( x + a ) " when n is a positive integer . Consider the expression ( x + α ) ( x + b ) ( x + c ) ...... ( x + k ) , the number of factors being n . The expansion of this expression is the continued product of the n factors ...
Página 315
... expansion of ( x + a ) " . 383. The coefficients in the expansion of ( x + a ) " are very conveniently expressed by the symbols " C1 , " C2 , " C , ... " C . We shall , however , sometimes further abbreviate them by omitting n , and ...
... expansion of ( x + a ) " . 383. The coefficients in the expansion of ( x + a ) " are very conveniently expressed by the symbols " C1 , " C2 , " C , ... " C . We shall , however , sometimes further abbreviate them by omitting n , and ...
Página 316
... expansion of ( 1 + x ) " . This is obtained from the general for- mula of Art . 382 , by writing 1 in the place of x ... expansion of a binomial may always be made to depend upon the case in which the first term is unity ; thus y ( x + y ) ...
... expansion of ( 1 + x ) " . This is obtained from the general for- mula of Art . 382 , by writing 1 in the place of x ... expansion of a binomial may always be made to depend upon the case in which the first term is unity ; thus y ( x + y ) ...
Página 318
... expansion ( a + x ) n = an + nan − 1x + We observe that in any term n ( n - 1 ) 1.2 ・ an - 2x2 . ( 1 ) The exponent of x , the second term of the binomial , is one less than the number of the term from the first . ( 2 ) The sum of the ...
... expansion ( a + x ) n = an + nan − 1x + We observe that in any term n ( n - 1 ) 1.2 ・ an - 2x2 . ( 1 ) The exponent of x , the second term of the binomial , is one less than the number of the term from the first . ( 2 ) The sum of the ...
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Términos y frases comunes
a+3b a+b+c a₁ a²+b² arithmetic means arithmetical arranged ascending powers b₁ beginner Binomial Theorem cents CHAPTER coefficients column compound expression continued fraction convergent cube root decimal denote digits dimes Divide dividend division divisor equal EXAMPLES XI Find the highest find the number Find the square Find the sum find the value following expressions given expressions greater harmonic mean Hence highest common factor integer less letters logarithm lowest common multiple method miles an hour Multiply number of terms numerator and denominator obtain partial fractions prefixed prove quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs second term Simplify SIMULTANEOUS EQUATIONS solution square root subtraction Suppose surds symbols Transposing unknown quantity walk whence write yards zero
Pasajes populares
Página 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 256 - In a quadratic equation wJiere the coefficient of the first term is unity, (i) the sum of the roots is equal to the coefficient of x with its sign changed ; (ii) the product of the roots is equal to the third term.
Página 168 - Thus the 4th root (2x2) = the square root of the square root ; the sixth root (3x2) = the cube root of the square root, or the square root of the cube root.
Página 178 - A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ? 17.
Página 179 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.
Página 280 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1...
Página 213 - Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the number of solutions. When positive integral values of the unknown quantities are required, the equations are called simple indeterminate equations. The introduction of this restriction enables us to express the solutions in a very simple form. Ex. 1....