Elements of Algebra with ExercisesMacmillan Company, 1902 - 478 páginas |
Dentro del libro
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Página xiv
... VARIABLES AND LIMITS . § 1 . VARIABLES § 2 . LIMITS 418 419 Fundamental Principles of Limits Infinites and Infinitesimals Indeterminate Fractions 421 422 422 CHAPTER XXXI . CONVERGENT AND DIVERGENT SERIES PAGE 424 CHAPTER xiv CONTENTS .
... VARIABLES AND LIMITS . § 1 . VARIABLES § 2 . LIMITS 418 419 Fundamental Principles of Limits Infinites and Infinitesimals Indeterminate Fractions 421 422 422 CHAPTER XXXI . CONVERGENT AND DIVERGENT SERIES PAGE 424 CHAPTER xiv CONTENTS .
Página xv
... Convergent 454 To reduce a Quadratic Surd to a Continued Fraction Application of Convergents 455 457 To reduce a Periodic Continued Fraction to an Irrational Number 458 • CHAPTER XXXV . LOGARITHMS . PAGE Irrational Powers 460 Solution ...
... Convergent 454 To reduce a Quadratic Surd to a Continued Fraction Application of Convergents 455 457 To reduce a Periodic Continued Fraction to an Irrational Number 458 • CHAPTER XXXV . LOGARITHMS . PAGE Irrational Powers 460 Solution ...
Página 423
... x1 . x3 - 2x + 2 ' a2x 1 8 . ах - 2 ac 9 . 10 . 2 ab - when x 0 . a2 + b2 - c2 a2 - b2 + c22 x2 + 2xy + y2 — z2 x2 + 2 xz - y2 + z2 ' when ca- b . when ( y + z ) . - CHAPTER XXXI . CONVERGENT AND DIVERGENT SERIES . 1. In $ 2 ] 423 LIMITS .
... x1 . x3 - 2x + 2 ' a2x 1 8 . ах - 2 ac 9 . 10 . 2 ab - when x 0 . a2 + b2 - c2 a2 - b2 + c22 x2 + 2xy + y2 — z2 x2 + 2 xz - y2 + z2 ' when ca- b . when ( y + z ) . - CHAPTER XXXI . CONVERGENT AND DIVERGENT SERIES . 1. In $ 2 ] 423 LIMITS .
Página 424
George Egbert Fisher, Isaac Joachim Schwatt. CHAPTER XXXI . CONVERGENT AND DIVERGENT SERIES . 1. In this chapter we ... Convergent , when the sum of the first n terms approaches a definite finite limit , as n increases indefinitely . An ...
George Egbert Fisher, Isaac Joachim Schwatt. CHAPTER XXXI . CONVERGENT AND DIVERGENT SERIES . 1. In this chapter we ... Convergent , when the sum of the first n terms approaches a definite finite limit , as n increases indefinitely . An ...
Página 425
... convergent when x is numerically less than 1. Evidently , when = 1 , the series is divergent . When x = -1 , we have 1-1 + 1−1 + ...... . The sum of n terms of this series is +1 or 0 , according as n is odd or even . The series is said ...
... convergent when x is numerically less than 1. Evidently , when = 1 , the series is divergent . When x = -1 , we have 1-1 + 1−1 + ...... . The sum of n terms of this series is +1 or 0 , according as n is odd or even . The series is said ...
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Elements of Algebra with Exercises George Egbert Fisher,Isaac Joachim Schwatt Sin vista previa disponible - 2016 |
Términos y frases comunes
a₁ a²b a²b² a²x a²x² ab² absolute value algebraic arithmetical arithmetical means assigned number ax² binomial coefficient Commutative Law complex number contain convergent courier cube root decimal definition denominator digits divided division divisor dollars equal equivalent EXERCISES exponent factors Find the values following expressions following principle geometrical progression given equation given system greater harmonical means illustrates the following inequality irrational number less Let x stand logarithm miles monomial multinomial multiplied negative number obtained parentheses positive integers positive number powers principal root problem quadratic equation quadratic surds quotient r₁ radicand rational number remainder required numbers satisfy second member Simplify solution Solve the equation square root Substituting summands symbolically unknown number whence wherein x²y yards
Pasajes populares
Página 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 356 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Página 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Página 414 - C„.r. That is, the number of combinations of n dissimilar .things r at a time is equal to the number of combinations of the n things n — r at a time.
Página 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 326 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards; but if the circumference of each wheel...
Página 166 - The product of two fractions is a fraction whose numerator is the product of the numerators of the given fractions, and whose denominator is the product of the given denominators.
Página 472 - We therefore have : (i.) The characteristic of the logarithm of a number greater than unity is positive, and is one less than the number of digits in its integral part.
Página 418 - Thus, 16 x2, ± -^/(a? — ж2), etc., are functions of x; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Página 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.