Higher AlgebraFisher and Schwatt, 1901 - 615 páginas |
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Página xv
... LIMITS . 453 Functions § 1. VARIABLES § 2. LIMITS Infinites and Infinitesimals . • 456 456 457 459 Fundamental Principles of Limits 460 Indeterminate Fractions 462 CHAPTER XXXIII . INFINITE SERIES . Methods of Comparison The General ...
... LIMITS . 453 Functions § 1. VARIABLES § 2. LIMITS Infinites and Infinitesimals . • 456 456 457 459 Fundamental Principles of Limits 460 Indeterminate Fractions 462 CHAPTER XXXIII . INFINITE SERIES . Methods of Comparison The General ...
Página xvi
... Limit to Error of Any Convergent 509 To reduce a Quadratic Surd to a Continued Fraction 510 Application of Convergents 512 • To reduce a Periodic Continued Fraction to an Irrational Number 513 CHAPTER XXXVII . SUMMATION OF SERIES . By ...
... Limit to Error of Any Convergent 509 To reduce a Quadratic Surd to a Continued Fraction 510 Application of Convergents 512 • To reduce a Periodic Continued Fraction to an Irrational Number 513 CHAPTER XXXVII . SUMMATION OF SERIES . By ...
Página xvii
... Limits to the Roots 569 . 572 Newton's Method 575 Derived Functions 577 Multiple Roots . 578 Graphic Representation 580 Greatest and Least Terms in ƒ ( x ) 587 Principle of Continuity 588 To find an Equation whose Roots are Less than ...
... Limits to the Roots 569 . 572 Newton's Method 575 Derived Functions 577 Multiple Roots . 578 Graphic Representation 580 Greatest and Least Terms in ƒ ( x ) 587 Principle of Continuity 588 To find an Equation whose Roots are Less than ...
Página 261
... limits . E.g. , x2 + 1 > 2 , only for values of x greater than 1 and less than -1 ; that is , for values of x between 1 and + , and between 1 and Absolute Inequalities . 11. Ex . 1. Prove that if a b , then a2 + b2 > 2 ab . We have ( a ...
... limits . E.g. , x2 + 1 > 2 , only for values of x greater than 1 and less than -1 ; that is , for values of x between 1 and + , and between 1 and Absolute Inequalities . 11. Ex . 1. Prove that if a b , then a2 + b2 > 2 ab . We have ( a ...
Página 262
... limits must a lie to satisfy the inequality - * > 5 £ – 10 ? Transferring terms , 4 x > 10 ; whence x < § , by Art . 7 ( ii . ) . That is , the inequality is satisfied by all values of x between § and -∞ . Ex . 2. What values of x ...
... limits must a lie to satisfy the inequality - * > 5 £ – 10 ? Transferring terms , 4 x > 10 ; whence x < § , by Art . 7 ( ii . ) . That is , the inequality is satisfied by all values of x between § and -∞ . Ex . 2. What values of x ...
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Higher Algebra George Egbert Fisher,Isaac J. 1867- jt. auth Schwatt Sin vista previa disponible - 2015 |
Términos y frases comunes
a₁ a²b a²x a²x² ab² algebraic arithmetical means arithmetical progression assigned number ax² b₁ binomial coefficient Commutative Law complex number continued fraction convergent corresponding cube root definition denominator determinant difference digits divided divisor equal equivalent EXERCISES exponent Find the values finite following expressions following principle geometrical progression given equation given expression given number given series given system greater harmonical means inequality integer irrational number less logarithm mantissa method miles multinomial multiplied negative number obtained parentheses positive integer positive number powers preceding article principal root quadratic equation quotient r₁ radicand rational number remainder required numbers result S₁ second member second term Simplify solution Solve the equation square root Substituting subtracted surds 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 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 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 64 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
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.
Página 456 - 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 364 - The volume of a gas varies inversely as the pressure when the temperature is constant. When the pressure is 15, the volume is 20; what is the volume when the pressure is 20 ? Let v stand for the volume and p for the pressure. Then from pv = k we obtain k = 300. Therefore pv = 300. Consequently, when p = 20, 20 v = 300 ; whence v = 15. EXERCISES III. If zee y, what is the expression for x in terms of y, 1.
Página 379 - Progression (AP), is a series in which each term, after the first, is formed by adding a constant number to the preceding term.
Página 204 - A system of linear equations has a definite number of solutions. (i.) When the number of equations is the same as the number of unknown numbers. (ii.) When the equations are independent and consistent.
Página 100 - The square of the sum of two numbers is equal to the square \ (¿ of the first, plus twice the product of the first and second, plus the J square of the second.